Crystal structure refinement and bonding patterns of CrB4: A boron-rich boride with a framework of tetrahedrally coordinated B atoms

Article abstract of DOI:10.1021/ic2018083

Crystals of chromium tetraboride, a recently proposed candidate superhard material, have been grown for the first time to allow for a first structure refinement of the compound [orthorhombic, space group Immm (No. 71), a = 474.82(8) pm, b = 548.56(8) pm, and c = 287.17(4) pm, R value (all data) = 0.018]. The previously proposed structure model is confirmed, and accurate interatomic distances are presented for the first time. First-principles electronic structure calculations emphasize the unique framework of three-dimensionally linked B atoms that are tetrahedrally coordinated and carry a slightly negative charge. All B-B bonding is of the 2-center 2-electron type. CrB₄ is metallic with a pseudogap at the Fermi level.

Full text of DOI:10.1021/ic2018083

COMMUNICATION
pubs.acs.org/IC
Crystal Structure Refinement and Bonding Patterns of CrB4:
A Boron-Rich Boride with a Framework of Tetrahedrally Coordinated
B Atoms
†
†
‡
‡
,†
Arno Knappschneider, Christian Litterscheid, Joshua Kurzman, Ram Seshadri, and Barbara Albert*
†
Eduard-Zintl-Institute of Inorganic and Physical Chemistry, Technische Universit €a t Darmstadt, Petersenstrasse 18,
6
4287 Darmstadt, Germany
‡
Materials Research Laboratory, Department of Chemistry & Biochemistry and Materials Department, University of California,
Santa Barbara, California 93106, United States
S Supporting Information
b
from Rietveld refinement), with about 10% CrB as a second
2
ABSTRACT: Crystals of chromium tetraboride, a recently
product. Gray-metallic crystals of the title compound (Support-
ing Information, Figure s1) were mounted on a diffractometer
(Fa. Stoe, Darmstadt, IPDS2). The data set was indexed in the
orthorhombic crystal system, and the structure determination
was performed in space group Immm. Results of the structure
investigation are given in Tables 1 and 2. The X-ray powder
diffractogram displaying results of the two-phase Rietveld refine-
ment is shown in the Supporting Information (Figure s2). The
crystal structure is shown in Figure 1. The structure proposed
proposed candidate superhard material, have been grown
for the first time to allow for a first structure refinement of
the compound [orthorhombic, space group Immm (No. 71),
a = 474.82(8) pm, b = 548.56(8) pm, and c = 287.17(4) pm,
R value (all data) = 0.018]. The previously proposed structure
model is confirmed, and accurate interatomic distances are
presented for the first time. First-principles electronic struc-
ture calculations emphasize the unique framework of three-
dimensionally linked B atoms that are tetrahedrally coordi-
nated and carry a slightly negative charge. All BÀB bonding
1
earlier is essentially correct, although interactomic distances are
in some error.
is of the 2-center 2-electron type. CrB is metallic with a
The lattice parameters correspond well with those that were
4
4
pseudogap at the Fermi level.
recently reported from first-principles calculations, as well as the
calculation reported in this work. BÀB distances were refined to
values between 171.1(8) pm and 184.9(6) pm.
hromium tetraboride, CrB , was discovered in 1968, and on
the basis of powder data of a mixture of several chromium
4
Compared with the distances formerly discussed for CrB
166 and 191 pm), those are more realistic values for 2e2c
4
C
1,3
(
boride phases, a structure was proposed that consists of three-
bonds (single) bonds between B atoms. The resulting framework
of corner- and edge-connected boron-centered tetrahedra of B
atoms is unique in the field of boron-rich materials. As can be
seen in Figure 1, the B atom framework consists of boatlike six-
rings, corrugated eight-rings, and four-rings that are almost
planar. Distorted hexagonal prisms are formed around the Cr
atoms. CrÀB distances are 209.9(3) pm (4Â) and 221.7(3) pm
1
dimensionally interconnected BB tetrahedra. Not much later,
4
almost the same structure model was suggested for the manga-
nese analogue, MnB , based on diffraction data of similar
4
2
quality. Although the title compound has raised interest of
theoreticians as an analogue to the hypothetical tetragonal
3
carbon net (tetragonal diamond) and has been described
recently as a potentially superhard material with exceptionally
(
8Â). As shown in the highlighted part of Figure 1, the
4
high computed shear moduli, the synthesis of CrB and MnB
4
4
coordination of the metal atoms bears similarities to the layered
was never successfully repeated. Samples of sufficient quality for
crystallographic examination or property measurement have so
far not been obtained. Malychev et al. reported a high-tempera-
structures of RuB and OsB , in which the metal atoms also
2
2
14
nestle into boatlike six-rings of B atoms. Such an arrangement
has been described as resulting in a particularly strong covalent
ture (900 °C) electrochemical synthesis of CrB , but no further
4
bonding between metal and B atoms and taken to explain the
5
À8
details of these samples have been made available.
Some of
15
(
anisotropic) ultraincompressibility of OsB2. In CrB , the
4
the phase diagrams of the CrÀB system report a CrB phase to be
4
layers of conjugated six-rings are, of course, also linked in the
third direction, thus resulting in a three-dimensional framework
that could be described as a tetragonal diamond. The title
compound can, therefore, indeed be expected to exhibit a
hardness and incompressibility of higher isotropic character than
that of osmium and ruthenium diboride.
9,10
stable up to 1500 °C.
The structure of these tetraborides is
highly unusual because it does not consist of electron-deficient
polyhedra with multicenter bonding that is typical for boron-rich
11À13
compounds with three-dimensional B atom frameworks.
We have grown single crystals of the title compound from the
elements chromium (260 mg, Chempur, 99.9%) and boron
To better understand the structure and bonding patterns in
this important compound, we have carried out first-principles
(
216.2 mg, H. C. Starck, 98À99%). A cold-pressed pellet was
placed in a silica ampule with 190 mg of iodine as a mineralizer.
The ampule was heated to 1027 °C for 14 days and then
quenched to room temperature. Single crystals and crystalline
Received: August 18, 2011
Published: October 10, 2011
powders of CrB proved to be the main product (close to 90%
4
r 2011 American Chemical Society
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dx.doi.org/10.1021/ic2018083
|Inorg. Chem. 2011, 50, 10540–10542

Inorganic Chemistry
COMMUNICATION
Table 1. Details on the Data Collection and Structure
Refinement of CrB4
structural formula
CrB
4
cryst syst, space group
lattice parameters a, b, c/pm
formula units
orthorhombic, Immm (No. 71)
474.82(8), 548.56(8), 287.17(4)
2
À6
3
cell volume/10 pm
74.80(2)
À3
calcd density/g cm
4.229
temperature/°C
20(3)
radiation, wavelength/pm
θ range/deg
Mo Kα, 710.73
5.7 À 28.9
no. of unique reflns/param
71/11
À1
μ/mm , abs corrn
6.969, refdelf
prism, 0.2 Â 0.2 Â 0.15, metallic
0.0176
3
cryst shape, size/mm , color
R (unique reflns)
Figure 2. ELF for the valence electrons of CrB . Strongly covalent
4
localization between B atoms points to the 2c2e bonding. An isosurface
of ELF = 0.75 is displayed within a single unit cell. The ELF plane is
projected halfway down the c axis of the unit cell and displays a complete
absence of localization (covalent bonding) between Cr and B.
wR2 (unique reflns)
GOF (unique reflns)
electron density min/max
0.0447
1.438
À0.588/+0.365
Table 2. Positional and Displacement Parameters of CrB
4
2
and Uiso Values (pm ), Defined as One Third of the Track of
a
the Orthogonalized Tensor Uij
Wyckoff
atom
Cr
site
x, y, z
0, 0, 0
U11, U22, U33, U12, U13, U22
2a
0.0039(5), 0.0037(6),
.0045(6), 0, 0, 0
0
B
8n
0.1933(9),
.3441(7), 0
0.035(2), 0.029(2),
0
0.007(2), 0.025(2), 0, 0
a
Figures in brackets are standard deviations that refer to the last digit.
4
Figure 3. Total and projected DOSs for CrB suggesting metallic
behavior and displaying a pseudogap at the Fermi energy.
crystallographic (rather than primitive) cell using a 10 Â 8 Â 14
Monkhorst-Pack k mesh and a plane-wave energy cutoff of 500 eV.
Relaxation was deemed to have converged when forces on all of the
À1
atoms were less than 0.01 eV Å . The geometry-optimized crystal
structure in space group Immm was as follows: a = 475.0 pm,
b = 548.9 pm, and c = 285.3 pm. Cr is on a special position. The
position of B optimized to (0.1954, 0.3423, 0). These optimized
parameters agree very well with the experimental data reported here
2
0
(
Table 2). Atomic charges determined by the Bader method with
21
the aid of the Bader analysis program suggested a charge close to
+
0.92 for Cr atoms and À0.23 for B atoms.
4
Figure 1. Crystal structure of CrB , showing B atoms as red, connected
spheres, and Cr atoms as green spheres. A portion of the upper part of the
Further details of the bonding were obtained by calculating the
electron localization function (ELF) within the linear muffin-tin
orbital (LMTO) method, as implemented in the Stuttgart TB-
LMTO-ASA program. The ELF was employed to understand
the localized bonding in the real space of the crystal struc-
ture.
picture of localized 2-center 2-electron (2c2e) bonds between
the B atoms as opposed to the more delocalized situation that
has been observed by experimental electron density analysis for
electron-deficient boron clusters.
figure is highlighted to accentuate a similarity with the OsB structure.
2
22
electronic structure calculations. Geometry optimization was
performed using the Vienna ab initio simulation package
23,24
The ELF, which is depicted in Figure 2, supports the
1
6
(
VASP) within the generalized gradient approximation of
17
Perdew, Burke, and Ernzerhof. Interaction between the valence
and core electrons was described using the projector augmented
wave approach,
1
8,19
24À26
and the semicore 3p states of chromium
The Cr atom does not
were treated as valence states. The structure was optimized in the
show a preferred interaction with its neighboring B atoms but
1
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Inorganic Chemistry
COMMUNICATION
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(
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’
ASSOCIATED CONTENT
(
S
Supporting Information. X-ray crystallographic data in
b
(23) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397–
CIF format, photograph of a silica ampule, and a powder pattern.
This material is available free of charge via the Internet at http://
pubs.acs.org. Further details of the crystal structure investigation
may be obtained from Fachinformationszentrum Karlsruhe,
5403.
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7
8
6344 Eggenstein-Leopoldshafen, Germany [fax (+49)7247-
08-666; e-mail crysdata(at)fiz-karlsruhe.de; web site http://
(
www.fiz-karlsruhe.de/request_for_deposited_data.html) upon
quoting the CSD number 423380.
’
AUTHOR INFORMATION
Corresponding Author
*E-mail: albert@ac.chemie.tu-darmstadt.de.
’
ACKNOWLEDGMENT
This work made use of the California NanoSystems Institute/
Materials Research Laboratory High Performance Computing
Facility, with funds provided by NSF Grants CHE-0321368 and
DMR-0520415 and by Hewlett-Packard. J.K. is thankful for the
ConvEne-IGERT Program (NSF-DGE 0801627) for an Asso-
ciateship. B.A. gratefully acknowledges financial support from the
Alexander von Humboldt Foundation and the German Aca-
demic Exchange Service.
’
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