Calcium tetraboride - Does it exist? Synthesis and properties of a carbon-doped calcium tetraboride that is isotypic with the known rare earth tetraborides

Article abstract of DOI:10.1021/ic0518430

Crystalline samples of carbon-doped CaB₄ were synthesized by solid-state reactions in sealed niobium ampules from the elements Ca, B, and C. The structure was determined by single-crystal X-ray diffraction (P4/mbm, Z = 4, a = 7.0989(7) A, c = 4.1353(5) A, R1 = 0.026, and wR2 = 0.058) revealing an atom arrangement containing a three-dimensional boron network built up from B₆ octahedra and B₂ dumbbells which is well-known from the structures of rare earth tetraborides. Crystals of CaB_4-xC_x are black with a metallic luster and behave stable against mineral acids. Band structure calculations indicate that CaB₄ is a stable semiconducting compound with a narrow band gap and that carbon should not necessarily be required for the stability of this compound. The presence of carbon in the crystalline samples of CaB_4-xC_x was indicated by electron energy loss spectroscopy, but the carbon content in the samples was estimated to be less than 5% according to inductively coupled plasma-atomic emission spectrometry measurements. The distribution of boron and carbon atoms in the structure was investigated by means of ¹¹B and ¹³C solid-state magic angle spinning NMR. Measurements of the magnetic susceptibility indicate a temperature-independent paramagnetism down to 20 K.

Full text of DOI:10.1021/ic0518430

Inorg. Chem. 2006, 45, 3067−3073
Calcium TetraboridesDoes It Exist? Synthesis and Properties of a
Carbon-Doped Calcium Tetraboride That Is Isotypic with the Known
Rare Earth Tetraborides
Ruth Schmitt, Bj o1 rn Blaschkowski, Klaus Eichele, and H.-J u1 rgen Meyer*
Institut f u¨ r Anorganische Chemie, UniVersit a¨ t T u¨ bingen, Auf der Morgenstelle 18,
D-72076 T u¨ bingen, Germany
Received October 25, 2005
Crystalline samples of carbon-doped CaB
4
were synthesized by solid-state reactions in sealed niobium ampules
from the elements Ca, B, and C. The structure was determined by single-crystal X-ray diffraction (P4/mbm, Z
)
4, a
)
7.0989(7) Å, c
)
4.1353(5) Å, R1
)
0.026, and wR2
)
0.058) revealing an atom arrangement containing
a three-dimensional boron network built up from B
6
2
octahedra and B dumbbells which is well-known from the
structures of rare earth tetraborides. Crystals of CaB
against mineral acids. Band structure calculations indicate that CaB
narrow band gap and that carbon should not necessarily be required for the stability of this compound. The presence
of carbon in the crystalline samples of CaB was indicated by electron energy loss spectroscopy, but the
carbon content in the samples was estimated to be less than 5% according to inductively coupled plasma atomic
4-x
C
x
are black with a metallic luster and behave stable
4
is a stable semiconducting compound with a
4-x x
C
−
emission spectrometry measurements. The distribution of boron and carbon atoms in the structure was investigated
by means of 11B and 13C solid-state magic angle spinning NMR. Measurements of the magnetic susceptibility
indicate a temperature-independent paramagnetism down to 20 K.
2
-
Introduction
saturation of the boron network as [B
6
] , and the surplus
electron accounts for the metallic conductivity.3
Divalent hexaborides (CaB , SrB , and EuB ), on the other
6 6 6
hand, are considered to be small-gap semiconductors, or
rather as semimetals, because of the overlap of an almost-
filled band with an almost-empty band near the X point at
the Fermi level. High-temperature ferromagnetism once
reported for the lanthanum-doped calcium hexaboride
turned out not to be an intrinsic property of this
material. Otani and Mori demonstrated that this effect
-6
6
The hexaborides MB of the alkaline earth elements (M
)
Ca, Sr, and Ba) and most of the rare earth elements (M )
7
1
Y, La-Er, Yb) are known and well-characterized. They
crystallize in a simple cubic structure with the space group
Pm 3h m, and their structures can be derived from the CsCl
8
6
structure, by replacing chloride with a B octahedron and
cesium with a respective metal atom. Each boron octahedron
in the structure is interconnected via apexes by covalent B-B
bonds with six adjacent clusters to form a three-dimensional
network. In this network structure, the B-B distances
between octahedral clusters are shorter than those within the
clusters.
Trivalent hexaborides of the rare earth elements exhibit
interesting physical properties and applications. One striking
6
example is the application of LaB as a cathode material in
9
Ca1-xLa B
x 6
1
0
resulted from iron impurities in the samples.
(
2) Lafferty, J. M. J. Appl. Phys. 1951, 22, 299-309.
(3) Walch, P. F.; Ellis, D. E.; Mueller, F. M. Phys. ReV. B 1977, 15, 1859-
866.
4) Kubo, Y.; Asano, S. Phys. ReV. B 1989, 39, 8822-8831.
(5) Booth, C. H.; Sarrao, J. L.; Hundley, M. F.; Cornelius, A. L.; Kwei,
1
(
G. H.; Bianchi, A.; Fisk, Z.; Lawrence, J. M. Phys. ReV. B 2001, 63,
224302/1-224302/8.
electron microscopy, as a result of its good thermoionic
emission properties. These hexaborides are metallic com-
pounds because only two electrons are necessary for the
(
6) Monnier, R.; Delley, B. Phys. ReV. B 2004, 70, 193403/1-193403/4.
2
(7) Longuet Higgins, H. C.; Roberts, M. d. V. Proc. R. Soc. London, Ser.
A 1954, 224, 336-347.
(
8) Massidda, S.; Continenza, A.; de Pascale, T. M.; Monnier, R. Z. Phys.
B: Condens. Matter 1997, 102, 83-89.
*
Author to whom correspondence should be addressed. E-mail:
(9) Young, D. P.; Hall, D.; Torelli, M. E.; Fisk, Z.; Sarrao, J. L.;
Thompson, J. D.; Ott, H.-R.; Oseroff, S. B.; Goodrich, R. G.; Zysler,
R. Nature 1999, 397, 412-414.
juergen.meyer@uni-tuebingen.de.
1) Zuckerman, J. J.; Hagen, A. P. Inorganic Reactions and Methods;
(
VCH Weinheim: Weinheim, Germany; Vol. 13, p 84.
(10) Otani, S.; Mori, T. J. Phys. Soc. Jpn. 2002, 71, 1791-1792.
1
0.1021/ic0518430 CCC: $33.50
© 2006 American Chemical Society
Inorganic Chemistry, Vol. 45, No. 7, 2006 3067
Published on Web 03/09/2006

Schmitt et al.
The related alkali carbaborides MB
form structures that are isotypic with the hexaborides,
5
C (M ) Na and K)
ratio of about 3:2). The best results were obtained when the molar
ratios of Ca/B/C were 3:2:1.
1
To explore another starting material, Ca was reacted with B C
however, with /
6
of the boron atoms substituted by a carbon
4
1
1,12
in a 3:1 molar ratio in tantalum tubes. All preparative handling
and the treatment after reaction were performed as before. The
reaction was carried out at 950 °C for 72 h. After cooling the
x
reaction down, CaB4-xC was obtained as the only product
detectable in the X-ray powder pattern.
To study the role of carbon in this reaction in more detail, a
atom.
Electron counting leads to 20 electrons for both
-
2-
[
B
5
C] in MB
The tetraborides MB
elements and crystallize with the ThB
Most of the rare earth tetraborides (M ) Nd, Sm, Gd, Tb,
Dy, and Ho) show antiferromagnetic behavior, while ErB
and YbB are metamagnetic. PrB is the only ferromagnetic
tetraboride.16 LaB
seems to have very similar electron
emitter qualities to those of LaB
Tetraborides of Sr, Ba, and Eu are unknown. Only a vague
5
C and [B
6
]
6
in CaB .
4
are prominent for trivalent rare earth
1
3-15
4
-type structure.
4
mixture of Ca and B
4
C was heated only at 800 °C and remained at
4
4
this temperature for 3 days. The powder XRD pattern of the product
19
20
4
2 2
revealed a mixture of â-rhombohedral boron, CaB C , and three
17
6
.
different modifications of calcium carbide. The relative intensities
of the strongest reflections in the XRD powder pattern of tetragonal
21
21
22
18
2 2 2 2 2
CaC (I), CaB C , monoclinic CaC (II), and monoclinic CaC (III)
indication was given for the existence of CaB
present the carbon-doped tetraboride CaB4-x
example of an alkaline earth boride with a ThB
structure.
4
.
Here, we
as the first
-type
corresponded to an approximate 4:2:2:1 ratio. This mixture was
converted into CaB4-x in a following heating procedure at
50 °C for 3 days.
Our various experiments also revealed that a higher reaction
temperature tends to produce calcium hexaboride. In this context,
our experiments also revealed that CaB4-x is gradually converted
into CaB (or possibly CaB C ) at temperatures around 1000 °C
C
x
C
x
4
9
Experimental Section
C
x
Synthesis. All manipulations for the synthesis of CaB4-x
x
C were
6
6-x
x
performed in an Ar-filled glovebox (MBraun) with Ca (Strem,
in an open vessel under Ar.
9
9.99%, dendritic), â-rhombohedral boron (ABCR, crystalline
X-ray Diffraction Studies. After being washed and dried, the
reaction products were ground and inspected with an X-ray powder
diffractometer (Stoe, StadIP, Darmstadt) using monochromatic Cu
KR1 radiation. The powder XRD pattern of the product synthesized
13
powder, 99.7%), graphite (Strem, carbon 5N), amorphous
C
(
Chemotrade, 99%), and B
starting materials.
was first obtained from reactions of Ca, B, and C in
:2:1 molar ratios in niobium containers. Graphite and boron
4
C (Riedel-de Ha e¨ n, X-ray pure) as
CaB4-x
C
x
from Ca and B C (Figure 1) was indexed with the aid of the
4
program system WinXPow (Stoe, Darmstadt),23 and the lattice
3
powders were thoroughly mixed in an agate mortar and then
transferred to a niobium container together with chunks of Ca metal.
The niobium container was sealed under Ar with an electric arc
and then sealed in an evacuated silica ampule. The samples, as
protected by two ampules, were heated to 1000 °C in a resistance-
heated box furnace (Carbolite) within 2 h and remained at this
temperature for 60 h. After cooling the furnace by its natural cooling
rate and opening the protecting containers, a black crystalline
material embedded into a matrix of excess Ca was obtained. This
material was isolated by washing the raw product in diluted
hydrochloric acid (pH 3-4). In this step, moisture-sensitive
parameters were refined using a tetragonal primitive indexing
scheme, yielding a ) 7.0625(6) Å and c ) 4.1207(4) Å (based on
39 reflections).
A single crystal of CaB4-xC prepared from Ca, B, and C was
x
selected and mounted in a glass capillary for an intensity measure-
ment with a single-crystal X-ray diffractometer (Stoe, IPDS,
Darmstadt). The structure solution and refinement were obtained
with the program package SHELX-9724 in the space group
P4/mbm. The structure refinement was performed with calcium and
boron atoms, leading to three distinct boron positions in the crystal
4
structure of CaB . After the anisotropic crystal structure refinement
byproducts were also removed that were possibly CaC
2
2 2
and CaB C ,
of CaB , the occupation factors of all boron atoms were refined,
4
which were detected as intermediates in the reaction at 800 °C. In
but they did not deviate from full occupancies within their standard
the as-obtained material, small crystals (which later turned out to
be CaB4-xC ) were selected under a microscope for a single-crystal
x
X-ray diffraction (XRD) analysis.
All attempts to prepare carbon-free samples from direct combi-
nations of Ca and B with different molar ratios, at reaction
temperatures between 800 and 1200 °C, and with different reaction
deviations. Attempts to refine the site occupation factors with boron
and carbon on the same position did not lead to reliable results, no
matter if one or all three sites were considered. Selected data of
the crystal and conditions of the data collection are given in Table
1; atomic positions and isotropic displacement parameters are
provided in Table 2; anisotropic displacement parameters are listed
in Table 3. Important interatomic distances are given in Table 4.
Analyses. All preparative results pointed out that the presence
of carbon is essential for the formation of calcium tetraboride.
However, the structure refinement did not give a clue on the
6
durations yielded exclusively CaB . Without the employment of
carbon in reactions, we found no trace of a calcium tetraboride
phase. After carbon was added to the reaction mixture, the calcium
tetraboride phase was always formed.
Our preparative explorations revealed that calcium tetraboride
is formed with a small amount of carbon and that yields can be
increased in the presence of an excess of calcium (minimum Ca/B
presence or distribution of carbon atoms in the structure. GdB
well as other rare earth tetraborides are reported to exist as pure
borides. When GdB was crystallized from the Gd-B-C system,
4
as
4
(
(
(
(
(
(
11) Albert, B.; Schmitt, K. Chem. Commun. 1998, 23, 2373-2374.
12) Albert, B.; Schmitt, K. Chem. Mater. 1999, 21, 3406-3409.
13) Zalkin, A.; Templeton, D. H. Acta Crystallogr. 1953, 6, 269-272.
14) Felten, E. J.; Bender, I.; Post, B. J. Am. Chem. Soc. 1958, 80, 3479.
15) Will, G.; Schaefer, W. J. Less-Common Met. 1979, 67, 31-39.
16) Buschow, K. H. J.; Creyghton, J. H. N. J. Chem. Phys. 1972, 57,
(19) Callmer, B. Acta Crystallogr., Sect. B 1977, 33, 1951-1954.
(20) Albert, B.; Schmitt, K. Inorg. Chem. 1999, 38, 6159-6163.
(21) Reckeweg, O.; Baumann, A.; Mayer, H. A.; Glaser, J.; Meyer, H.-J.
Z. Anorg. Allg. Chem. 1999, 625, 1686-1692.
(22) Glaser, J.; Dill, S.; Marzini, M.; Mayer, H. A.; Meyer, H.-J. Z. Anorg.
Allg. Chem. 2001, 627, 1090-1094.
3910-3914.
(23) WinXPow, version 1.10; Stoe&Cie GmbH: Darmstadt, Germany, 2001.
(24) Sheldrick, G. M. SHELX-97; University G o¨ ttingen: G o¨ ttingen,
Germany, 1997.
(17) Deacon, J. A.; Hiscocks, S. E. R. J. Mater. Sci. 1971, 6, 309-312.
18) Johnson, R. W.; Daane, A. H. J. Chem. Phys. 1961, 65, 909-915.
(
3068 Inorganic Chemistry, Vol. 45, No. 7, 2006

Calcium Tetraboride
Figure 1. Comparison of the recorded (above) and calculated (below) X-ray powder patterns of CaB4-xCx. The peak at 2θ ) 43° is due to the sample
preparation.
2
Table 1. Crystal Data and Parameters for Data Collection and
Table 3. Anisotropic Displacement Parameters (pm ) in CaB4
Structure Refinement for CaB4
atom position
U11
U22
U33
U23
U13
U12
sum formula, units per unit cell
fw/(g/mol)
temp/K
radiation, wavelength/Å,
monochromator
space group
CaB4, 4
83.32
293(2)
Mo KR, 0.71073,
graphite
P4/mbm (No. 127)
a ) 7.0989(7)
c ) 4.1353(5)
208.40(4)
2.656
2.53
10 e 2Θ e 65
-10 e h e 10,
Ca
4g
8j
4h
4e
118(2) 118(2) 130(2)
118(8) 117(8) 85(7)
119(8) 119(8) 113(10)
123(8) 123(8) 89(9)
0
0
0
0
0
0
0
0
18(1)
-3(5)
-10(7)
0
B(1)
B(2)
B(3)
Table 4. Selected Interatomic Distances (in Å) in the Crystal Structure
of CaB4
cell dimensions/Å
cell volume/Å3
B(1)-B(1) 1.822(2)
B(3)-B(1) 1.773(2)
B(2)-B(2) 1.670(5)
B(3)-B(3) 1.697(4)
B(1)-B(2) 1.729(2)
2× B6 octahedra
3
calcd density/(g/cm )
4×
-
1
abs coeff (mm
)
1× B2 dumbbell
measured range/deg
index ranges
1× connection octahedra-octahedra
2× connection octahedra-dumbbell
-
10 e k e 10,
6 e l e 6
Ca-B
2.738(1)-3.142(2) 16× CaB16 polyhedra
-
observed reflns
2298
EELS. From the EEL spectrum (Gatan PEELS666 spectrometer),
characteristic energy losses were found for Ca, B, and C. Although
reliable quantitative elemental analyses from EEL spectra are only
possible with suitable reference materials, a small amount of carbon
was estimated from the EELS data, besides Ca and B (Figure 2).
independent reflns
240 (Rint ) 0.034)
0.0231, 0.0571
0.50 and -0.35
a
R1, wR2 [I > 2σ(I)]
residual electron density/
-
6
-3
(
10 e pm
)
a
2
2 2
2 2
R1 ) (∑hkl||Fo| - |Fc||)/∑hkl|Fo|; wR2 )
x
∑hklw(F -F ) /∑ w(F ) .
o c hkl o
ICP-AES. Quantitative analyses of the carbon content were
performed by means of ICP-AES (LECO CS-444LS) measure-
Table 2. Atomic Coordinates and Isotropic Displacement Parameters in
CaB4
ments. CaB4-x
C
x
samples used for the analyses were prepared in
atom position
x/a
y/b
z/c
Uiso (pm2)
4
two different batches, using Ca and B C as starting materials. Both
products occurred as single-phase materials, according to their
powder XRD pattern. For each experiment, a 5 mg sample was
Ca
4g
8j
4h
4e
0.31884(4) 0.818 84(4)
0
1/2
1/2
122(2)
107(5)
117(7)
112(7)
B(1)
B(2)
B(3)
0.1780(2)
0.4168(2)
0
0.0353(2)
0.0831(2)
0
solubilized with 0.5 mg of Na
was dissolved in 2 mL of HNO
AES measurement. The total carbon content was refined as 3.0
and 3.8 wt % from two different samples of CaB4-x . This
corresponds to CaB4-x with x ) 0.21 and 0.26, respectively.
NMR. Solid-state 11B and 13C magic angle spinning (MAS)
NMR experiments on CaB4-x were carried out at 4.7 T (Bruker
2
CO
3
3
and 0.2 g of KNO . This mixture
0.2052(5)
3
and then diluted for the ICP-
it showed only very small amounts (<1%) of carbon in the boron
C
x
network, according to (WDS-EPMA) analyses.25 To learn more
C
x
x
about the role of carbon in CaB4-xC , more experiments such as
electron energy loss spectroscopy (EELS), inductively coupled
plasma-atomic emission spectrometry (ICP-AES), and solid-state
NMR were carried out.
C
x
11
13
DSX 200, 4 mm o.d. zirconia rotors; B, 64.21 MHz; C, 50.32
MHz) and 11.75 T (Bruker Avance 500, 2.5 mm o.d. zirconia rotors;
B, 160.51 MHz; C, 125.80 MHz). Chemical shifts are reported
for 11B with respect to F
B‚OEt using NaBH (-42.06 ppm) as
11
13
(25) Garland, M. T.; Wiff, J. P.; Bauer, J.; Gu e´ rin, R.; Saillard, J.-Y. Solid
State Sci. 2003, 5, 705-710.
3
2
4
Inorganic Chemistry, Vol. 45, No. 7, 2006 3069

Schmitt et al.
Figure 2. Electron energy loss spectrum showing the CaL2,3, BK, and CK
edges.
an external secondary reference and for 13C with respect to
tetramethylsilane using adamantane (38.55 ppm, CH) as an external
13
secondary reference. Samples for C measurements were prepared
with calcium, boron, and 100% 13C as starting materials.
For comparison with CaB4-x
NMR spectrum of a separately prepared sample of LaB
). The 11B MAS NMR spectrum of LaB
shows two isotropic peaks
C
x
, we also obtained the 11B MAS
(Figure
4
3
4
at 39 and 12 ppm in a 1:1 ratio for the central transitions. However,
a closer examination of the spinning sideband pattern associated
with the 11B satellite transitions reveals that the sideband manifold
at higher frequencies actually consists of two equally populated
sites with significantly different nuclear quadrupolar coupling
2
6
constants. Analysis of the satellite transitions yields nuclear
2
quadrupolar coupling constants, ø ) e qZZQ/h, and asymmetry
parameters of the electric field gradient tensor, η ) (qXX - qYY)/
2
7
q
ZZ
,
that are in excellent agreement with those reported by
28
4
Creyghton et al. for a static powder sample of LaB at 4.2 K.
Because of the limited resolution of 11B static powder spectra,
Creyghton et al. were not able to determine the different chemical
shifts of the boron sites. In the present study, we obtained the
following data (with chemical shifts corrected for second-order
quadrupolar shifts): δiso ) 42 ppm, ø ) 0.69 MHz, η ) 0.00 (site
4
1
e); δiso ) 47 ppm, ø ) 1.1 MHz, η ) 0.05 (site 4h); δiso
8 ppm, ø ) 0.8 MHz, η ) 0.5 (site 8j).
)
Figure 3. 11B MAS NMR spectra obtained at 4.7 T for LaB4, simulated
using the parameters given in the text (a) and observed (b), and for CaB4-xCx
4 x
Similar to LaB C
, the 11B MAS NMR spectrum of CaB4-x
features two different isotropic peaks at 56 and 5 ppm for the central
transitions, but the intensity ratio is 0.8:1. Again, the peak at 5
ppm is assigned to site 8j, with δiso ) 11 ppm, ø ) 0.8 MHz, and
η ) 0.3 (Figure 3). The spinning sidebands associated with the
satellite transitions of 4e and 4h are very broad and, thus, much
weaker in intensity. This finding suggests that a distribution rather
than a unique set of quadrupolar parameters contributes to their
appearance, possibly caused by disorder of the incorporated carbon
atoms. Disorder is also the likely reason for the observed field
(c). Spinning rate: 10 kHz. The central transitions were cut off at 10%
intensity.
Electronic Properties. The bonding properties and the electronic
situation in CaB4-x were investigated by extended H u¨ ckel
calculations (YAeHMOP ) of the band structure on the basis of
the refined crystal structure data of CaB4-x . Calculations were
first performed under the assumption of a pure boride network
containing four formula units of CaB in the unit cell and cyclic
C
x
29
C
x
4
boundary conditions. Changes in the electronic structure resulting
from substitutions of boron atoms versus carbon atoms in the
structure were studied afterward. Band structure calculations within
the tetragonal primitive Brillouin zone were performed at 20 k points
along each symmetry line connecting the special points Γ ) (0,0,0),
13
dependence of the line width of the peak at 136 ppm in the
MAS NMR spectrum of 13C-enriched CaB4-x
(Figure 4), that is,
300 Hz at 4.7 T and 2800 Hz at 11.75 T.
Magnetic Studies. The magnetic susceptibility behavior of
was studied with a SQUID magnetometer (Quantum
C
C
x
1
CaB4-xC
x
1
1
1
1
1
1
1
X ) (0, /
2
,0), M ) ( /
2
2
, /
2
,0), A ) ( /
2
, /
2
, /
2
2
), Z ) (0,0, / ), and R
Design, MPMS) in the temperature region between 20 and 300 K
using a static field (H ) 1000 G). The measurements revealed a
temperature-independent paramagnetic behavior with a susceptibility
1
1
30
)
(0, /
2
, /
). A set of 288 k points in the first reduced Brillouin
zone was used for calculations of the average properties (density
of states, DOS, and crystal orbital overlap population, COOP). The
parameters employed in the calculations were adopted from the
literature.29
-
3
3
on the order of ømol ) 1 × 10 cm /mol.
(
(
(
26) Eichele, K. Csolids, version 1.4.26; University of T u¨ bingen: T u¨ bingen,
Germany, 2005.
27) Abragam, A. Principles of Nuclear Magnetism; Clarendon Press:
Oxford, U. K., 1961.
(29) YAeHMOP, extended H u¨ ckel molecular orbital package, freely
available on the Web at http://sourceforge.net/projects/yaehmop.
(30) Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry
in Solids; Claredon Press: Oxford, U. K., 1972; pp 82-109.
28) Creyghton, J. H. N.; Locher, P. R.; Buschow, K. H. J. Phys. ReV B
1973, 7, 4829-4843.
3070 Inorganic Chemistry, Vol. 45, No. 7, 2006

Calcium Tetraboride
Figure 4. 13C MAS NMR spectrum of CaB4-xCx obtained at 4.7 T and with a spinning of 10 kHz.
Results and Discussion
Structure. The single-crystal structure refinement of
CaB4-xC revealed a ThB -type structure that is well-known
x 4
for many rare earth tetraborides. Boron atoms in this structure
occupy three distinct special positions: B(1) occupies an 8j
position and forms squares, B(2) occupies a 4h position and
forms dumbbells, and B(3) is on a 4e position bicapping the
squares to complete tetragonal B
carbon content in CaB4-x is relatively low, and may be
expressed as CaB3.8 0.2 according to chemical analyses, the
6
bipyramides. Because the
C
x
C
crystal structure is discussed simply as calcium tetraboride,
which should, in fact, exist, as will be explained later.
The crystal structure of CaB
of slightly (D4h) distorted B octahedra [dB-B ) 1.822(2) Å
2×) and 1.773(2) Å (4×)] and ethylene-like B dumbbells
B-B ) 1.670(5) Å], which are combined into a three-
4
contains a boron network
6
(
[
2
d
dimensional network. A projection on the ab plane of the
structure shows the connectivity of distorted boron octahedra
and dumbbells forming a two-dimensional layer, displayed
in Figure 5. The B-B bond lengths between octahedra and
dumbbells are 1.729(2) Å. The seven-membered rings in this
structure pattern are capped with Ca ions from above and
below, with Ca ions being situated in a 16-fold environment
Figure 5. Connectivity of B6 octahedra and B2 dumbbells in the ab plane
in the crystal structure of CaB4. Ca is shown gray and B black.
into fragments of closo-B
A closo-B cluster requires (4n + 2) 14 electrons, and the
ethylene-like B unit requires four electrons. When these
fragments are being linked via B-B single bonds, six
additional electrons for each B cluster and four additional
electrons for each ethylene-like B unit are required. When
the unit cell content (Z ) 4) of M (B (B is
considered with two B octahedra and two B dumbbells,
6 electrons are required for the stabilization of the boron
network. This exactly matches the number of valence
electrons in Ca 16. It can be, therefore, assumed that
tetraborides possessing the ThB -type structure occur as
6 2
clusters and ethylene-like B units.
[d
Ca-B ) 2.738(1)-3.142(2) Å] of boron atoms. A view
along the c-axis direction shows the apical connectivity of
distorted B octahedra (Figure 6) with B-B bond lengths
6
2
6
of 1.697(4) Å.
Electronic Considerations. The electronic requirement
6
2
of the boron network in MB
6
hexaborides is generally
] , similar to that in the molecular
species. Consequently, hexaborides with divalent
4
B
16 or M
4
6
)
2
2 2
)
2-
considered to be [B
6
6
2
2-
6 6
[B H ]
5
2+
2-
cations occur as M [B
with trivalent cations may be considered as M [B
metals, because of one excess electron per formula unit. The
electronic situation of tetraborides with the ThB -type
structure has been proposed by Lipscomb and Britton.
Following this concept, the MB structure is first decomposed
6
]
semiconductors, whereas those
3+
2-
-
6
] ‚(e )
4
B
4
4
stable compounds with a divalent cation.
3
1
4
(31) Lipscomb, W. N.; Britton, D. J. Chem. Phys. 1960, 33, 275-280.
Inorganic Chemistry, Vol. 45, No. 7, 2006 3071

Schmitt et al.
Figure 8. Calculated total DOS of CaB4. The DOS contribution of B6
octahedra to the total DOS is shown as a lined area.
Figure 6. Connectivity of the B6 octahedra along the c-axis direction in
the crystal structure of CaB4.
Figure 9. COOPs for B6 octahedra (left) and B2 dumbbells (right) in the
structure of CaB4.
the B
orbitals of the B
up to the Fermi level (indicating a B-B double bond) and
strong antibonding π* interactions above ꢀ . A Mulliken
analysis carried out for both fragments leads to reduced
overlap populations of 0.58 for the B octahedra and 1.18
for the B dumbbell up to ꢀ . This finding supports the
assumption of ethylene-like [B octahedra,
2
unit is remarkable. A closer examination of the crystal
2
unit reveals strong bonding π interactions
Figure 7. Calculated band structure of CaB4 along several special points
of the first Brillouin zone for a primitive tetragonal lattice.
F
Electronic Properties. The band structure of CaB
4
was
6
calculated along several directions of the reciprocal space
and is displayed in Figure 7. The calculations revealed a very
small indirect band gap on the order of 0.2 eV above the
2
F
-
]2 units and [B
2-
2
6
]
which are interconnected with each other via B-B single
Fermi level (ꢀ
F
, shown as dotted line). All of the energy
bonds into a three-dimensional boron network. A simplified
charge picture can be postulated as (Ca ) [B ] [B ] . The
2 6 2
results of our extended H u¨ ckel calculations fully confirm
the closed-shell assumption proposed by Lipscomb and
Britton, which requires a divalent cation for the stabilization
2+
2-
2-
bands in the depicted area are dominated by orbital contribu-
tions from boron atoms. Orbital contributions of Ca play only
a minor role in the region around the Fermi level because
their empty 4s orbitals are at higher energies. Ca as a divalent
cation hardly takes part in covalent interactions with the
boron network. This behavior is in clear contrast to the
4
of the boron network in ThB -type structures.
In the next step, calculations were performed on structural
models in which boron atoms were partially substituted by
carbon atoms, first on one and then on all three distinct
positions. Because of the increased number of electrons, the
Fermi level went up to higher energy, leading to occupations
of antibonding orbitals in the boron/carbon network. In any
case, the largest impact on bonding properties was found
for the B unit, where the partial occupations of π* orbitals
2
caused a weakening of B-B bonding, for example, with a
reduction in the overlap populations down to 0.80 for
electronic structure of GdB
4
, where the d orbitals of Gd
interact with orbitals of the boron network, as we will
2
5
describe later.
An analysis of the energy bands shows varying orbital
contributions of the constituting fragments (B octahedra and
dumbbells) of the boron network. In Figure 8, the total
DOS and the respective contribution of the B octahedra are
shown. In the area slightly above the Fermi level, a relatively
low contribution of B states can be seen. A further analysis
6
B
2
6
6
of the COOPs shows transitions from B-B bonding interac-
tions below the Fermi level to B-B antibonding interactions
above, for both fragments (Figure 9). In particular, the
transition from strong bonding to strong antibonding within
0,25
CaB3,75C .
2 4
The bonding in the B unit in the structure of GdB is
weakened through electron donations of B-B π bonding into
Gd d orbitals. Despite the sp hybridization of each B atom
2
3072 Inorganic Chemistry, Vol. 45, No. 7, 2006

Calcium Tetraboride
in the B
considered between atoms of the dumbbell. A comparison
of the B-B bond lengths in CaB and those of the rare earth
tetraborides supports this assumption. For CaB , the B-B
distance in the B dumbbell is 1.670(5) Å, whereas in the
rare earth tetraborides MB (M ) Y, La, Ce, Nd, Sm, Gd,
Tb, Dy, and Er), the average distance in the B dumbbell
increases by about 8 pm to 1.752 Å. All of the other B-B
bonding interactions in CaB show only minor deviations
2
unit, there is, rather, a B-B single bond to be
25
4
4
2
4
2
4
Figure 10. Hypothetical activation barriers and relative stabilities of CaB4
and CaB6.
from average values found for the rare earth tetraborides.
From the calculated band gap of 0.2 eV, we assume
4 x
semiconducting behavior for CaB . Carbon-doped CaB4-xC
is, however, expected to behave as metallic. This is in
agreement with both the obtained metallic luster and the
differences in the bonding behavior of the dumbbells. Here,
the π orbitals of the dumbbells overlap with the d orbitals
of the lanthanide ions, and a pronounced increase of the
electrical conductivity can be regarded from the electron
delocalization over these orbitals. This finding is consistent
temperature-independent paramagnetic behavior of ømol
)
-
3
3
1
× 10 cm /mol in the temperature range between 20 and
300 K. Measurements of the electrical conductivity are not
with the 8-pm-shorter B-B distance in the dumbbell of CaB
We note a similar interaction for lanthanide dicarbides, for
example, in LaC . In this case, interactions between the
C-C antibonding) π* orbitals of dicarbide dumbbells and
the La d orbitals also relate to an 8-pm-shorter C-C distance
in the isotypic CaC
4
.
available because of intrinsic adhesion problems between
crystals and several fluid contact media.
2
(
Conclusion
6 6
The existence of isotypic structures for CaB and LaB
2
.
and their distinct properties as semiconducting and metallic
materials are well-known. The electronic requirement of an
isolated network of boron octahedra as present in these
Although the role of carbon in the reaction is to date not
well understood, one hypothesis could be that the formation
of pure calcium tetraboride from calcium and boron is
hindered kinetically as well as thermodynamically (Figure
2-
structures is considered to be [B
of lanthanide tetraborides, such as LaB
structure composed of boron octahedra and boron dumbbells
La [B ](B ]). The existence of a corresponding CaB
counterpart of LaB has remained unknown until now.
The structure of the carbon-doped calcium tetraboride is
isotypic with the structure of LaB . The carbon content of
is rather low (<5%), but the presence of carbon
6
] . The crystal structure
4
, contains a network
1
0). The presence of carbon in the reaction and the formation
of CaC and CaB as intermediates may allow a moderate
reaction pathway to yield a carbon-doped CaB
poses into (thermodynamically stable) CaB
2
2 2
C
(
2
6
2
4
4
that decom-
at elevated
4
6
temperatures (g1000 °C). In this context, it may be
worthwhile to note that the formation of higher borides is
also a problem in the synthesis of MgB , resulting from the
2
evaporation of Mg metal at elevated temperatures.
4
CaB4-xC
x
turned out to be essential for the synthesis of this compound.
Upon first glance, it could be assumed that carbon may
have a stabilizing effect by achieving the same valence
Acknowledgment. The authors express their thanks to
Dr. K. Hofmann and Prof. B. Albert (Universit a¨ t Hamburg,
Germany) for their valuable support with EELS measure-
ments. We are very grateful to Prof. T. Mori (National
Institute for Materials Science, Tsukuba, Japan) for generous
help with ICP-AES analyses. Prof. R. E. Wasylishen
(University of Alberta, Canada) is acknowledged for instru-
ment time on the Avance 500. R.S. gratefully acknowledges
a fellowship from the Studienstiftung des Deutschen Volkes.
3 4
electron number (“CaB C”) as that for LaB . This simple
consideration does not, however, satisfy the distinct bonding
requirements with cations in both types of compounds.
Theoretical considerations and band structure calculations
have demonstrated that CaB can be regarded as an elec-
4
tronically stable compound, eventually even more stable than
carbon-doped calcium tetraboride. The electronic charge
picture of CaB
dumbbells is approximated as (Ca )
ethylene-like B
B-B double-bonding interactions in CaB
4
with the constituting B
6
octahedra and B
[B ] [B ] . The
6 2
2
2+
2-
2-
2
Supporting Information Available: Additional tables and
crystallographic data in cif format. This material is available free
of charge via the Internet at http://pubs.acs.org.
2
dumbbell displays clear characteristics of
, although this type
4
of bonding is not well-established in boron chemistry.
Moving to the corresponding lanthanide tetraborides, we note
IC0518430
Inorganic Chemistry, Vol. 45, No. 7, 2006 3073