Preparation and properties of metallic, superhard rhenium diboride crystals

Article abstract of DOI:10.1021/ja804989q

Single crystals of ReB₂ have been prepared from an aluminum flux under inert gas flow. The crystals are typically 1-3 mm in diameter and 500 μm thick, growing along the [002] direction with a distinct hexagonal morphology. Vickers microhardness and nanoindentation testing indicate that the (002) plane possesses the highest hardness with measured values of 40.5 and 36.4 GPa, respectively. The elastic anisotropy was examined and the indentation moduli of the basal plane and an (MO) plane of unknown indices are 675 and 510 GPa, respectively. Four-probe electrical resistivity measurements demonstrate that ReB₂ is the hardest material known to exhibit metallic behavior. Thermogravimetric analysis indicates that the crystals are stable in air up to 1000°C due to the formation of a protective boron oxide coating.

Full text of DOI:10.1021/ja804989q

Published on Web 11/18/2008
Preparation and Properties of Metallic, Superhard Rhenium
Diboride Crystals
†
†
†
‡
Jonathan B. Levine, Sandy L. Nguyen, Haider I. Rasool, Jeffrey A. Wright,
‡,§
,†,§
Stuart E. Brown, and Richard B. Kaner*
Department of Chemistry & Biochemistry and Department of Physics & Astronomy,
UniVersity of California, Los Angeles, Los Angeles, California 90095
Received June 30, 2008; E-mail: kaner@chem.ucla.edu
2
Abstract: Single crystals of ReB have been prepared from an aluminum flux under inert gas flow. The
crystals are typically 1-3 mm in diameter and 500 µm thick, growing along the [002] direction with a distinct
hexagonal morphology. Vickers microhardness and nanoindentation testing indicate that the (002) plane
possesses the highest hardness with measured values of 40.5 and 36.4 GPa, respectively. The elastic
anisotropy was examined and the indentation moduli of the basal plane and an (hk0) plane of unknown
indices are 675 and 510 GPa, respectively. Four-probe electrical resistivity measurements demonstrate
that ReB
2
is the hardest material known to exhibit metallic behavior. Thermogravimetric analysis indicates
that the crystals are stable in air up to 1000 °C due to the formation of a protective boron oxide coating.
9
,18,19
Introduction
zone furnace.
properties of ReB
However, an extended study of the physical
has not been performed.
2
The binary transition metal borides have been the focus of
attention for decades because of their useful mechanical and
electrical properties. MgB
be superconducting at 39 K. Additionally, HfB
exhibit high hardness and good thermal stability,
is ultra-incompressible. Rhenium diboride, originally synthe-
sized in the 1960s, is a refractory compound with a melting
point of 2400 °C that was reported by our group to be an ultra-
incompressible, superhard material (hardness g 40 GPa).
2
Recently, thin films of ReB were prepared by pulsed laser
deposition that were also shown to be superhard. Since our
initial publication, there have been several theoretical studies
reported on the electrical, thermal, and rheological properties
The use of single crystals is important for measuring the
intrinsic properties of a material, as these properties are altered
by grain boundaries in polycrystalline samples. Furthermore,
1
2
, for example, has been reported to
2
2
, ZrB
2
, and TiB
and OsB
2
3
-5
2
because the layered crystal structure of ReB lends itself to
2
6
anisotropy, its physical properties, such as hardness, vary with
crystallographic orientation. Measurements performed on single
crystals allow separate characterization of a material’s individual
lattice planes. Knowledge of the mechanical anisotropy of a
material is also potentially useful for applications and effective
theoretical modeling of superhard materials. Here, we report
7
8
9
1
0
the synthesis and characterization of ReB
by a flux technique.
2
single crystals grown
of ReB
of properties.
2
to better understand this material’s unique combination
Experimental Section
11-17
2
To date, ReB crystals have been synthesized
Synthesis. Powders of rhenium metal (Rhenium Alloys, Inc.,
by arc melting, by zone melting, and using an optical floating
9
9.99%) and amorphous boron (Cerac, Inc., 99.9%) were added to
†
an alumina crucible containing an excess of aluminum (Cerac,
99.999%) as the growth medium. Using 2 g of Re, the molar ratio
of Re/B/Al was fixed at 1:2:50. The crucible was covered and placed
in an alumina tube in a resistively heated furnace with flowing Ar
gas. The furnace was heated to 1400 °C at a rate of 100 °C/h, held
there for 5 h, slowly cooled to 700 °C at a rate of 10 °C/h, and
Department of Chemistry & Biochemistry.
Department of Physics & Astronomy.
California NanoSystems Institute.
‡
§
(
(
(
1) Aronsson, B.; Lundstr o¨ m, T.; Rundqvist, S. Borides, Silicides, and
Phosphides; Methuen: London, 1965.
2) Nagamatsu, J.; Nakagawa, N.; Muranaka, T.; Zenitani, Y.; Akimitsu,
J. Nature 2001, 410, 63–64.
3) Kalish, D.; Clougherty, E. V.; Kreder, K. J. Am. Ceram. Soc. 1969,
5
2, 30–36.
(12) Zhou, W.; Wu, H.; Yildirim, T. Phys. ReV. B: Condens. Matter 2007,
76, 184113/1–184113/6.
(
(
(
4) Bsenko, L.; Lundstr o¨ m, T. J. Less-Common Met. 1974, 34, 273–278.
5) Munro, R. G. J. Res. Natl. Inst. Stand. Technol. 2000, 105, 709–720.
6) Cumberland, R. W.; Weinberger, M. B.; Gilman, J. J.; Clark, S. M.;
Tolbert, S. H.; Kaner, R. B. J. Am. Chem. Soc. 2005, 127, 7264–
(13) Liang, Y.; Zhang, B. Phys. ReV. B: Condens. Matter 2007, 76, 132101/
1–132101/4.
(14) Chen, X.-Q.; Fu, C. L.; Krcmar, M.; Painter, G. S. Phys. ReV. Lett.
7
265.
2008, 100, 196403/1–196403/4.
(
(
7) La Placa, S.; Post, B. Acta Crystallogr. 1962, 15, 97.
(15) Hao, X. F.; Xu, Y. H.; Wu, Z. J.; Zhou, D. F.; Liu, X. J.; Cao, X. Q.;
Meng, J. Phys. ReV. B 2006, 74, 224112.
8) Okamoto, H. Phase Diagrams for Binary Alloys, Desk Handbook;
2
000; Vol. 1.
(16) Hao, X. F.; Wu, Z. J.; Xu, Y. H.; Zhou, D. F.; Liu, X. J.; Meng, J. J.
Phys.: Condens. Matter 2007, 19, 196212.
(
9) Chung, H.-Y.; Weinberger, M. B.; Levine, J. B.; Kavner, A.; Yang,
J.-M.; Tolbert, S. H.; Kaner, R. B. Science 2007, 316, 436–439.
(17) Wang, Y. X. Appl. Phys. Lett. 2007, 91, 101904.
(18) Lyashchenko, A. B.; Paderno, V. N.; Filippov, V. B.; Borshchevskii,
D. F. SVerkhtVerd. Mater. 2006, 79–81.
(
(
10) Latini, A.; Rau, J. V.; Ferro, D.; Teghil, R.; Albertini, V. R.; Barinov,
S. M. Chem. Mater. 2008, 20, 4507–4511.
11) Zhang, R. F.; Veprek, S.; Argon, A. S. Appl. Phys. Lett. 2007, 91,
(19) Otani, S.; Aizawa, T.; Ishizawa, Y. J. Alloys Compd. 1997, 252, L19–
L21.
2
01914/1–201914/3.
10.1021/ja804989q CCC: $40.75

2008 American Chemical Society
J. AM. CHEM. SOC. 2008, 130, 16953–16958 9 16953

A R T I C L E S
Levine et al.
Figure 1. (A) Optical image of an as-grown ReB
2
crystal synthesized in an aluminum flux. Hexagonal growth patterns are clearly visible on the crystal
surface. (B) Scanning electron micrograph image of a ReB crystal grown in an aluminum flux (scale bar ) 100 µm).
2
then quickly cooled to room temperature. The aluminum flux was
then dissolved in 6 M NaOH, and the resulting products were
filtered with deionized water and dried in air.
Characterization. Powder X-ray diffraction patterns were col-
lected on a XPert Pro powder diffractometer with Cu KR radiation
2A). The lattice parameters were determined by Rietveld
refinement with the JADE software package (version 6.0), and
the values are in good agreement with those originally reported
7
by La Placa and Post, a ) 2.897(2) Å, c ) 7.472(4) Å, with
a final Rwp of 12.75%. The slightly high value for the R-factor
can be attributed to preferred orientation effects of the crushed
crystals. This report presents the first synthesis of any superhard
material by flux crystal growth under ambient pressure.
(
λ ) 1.5418 Å; PANalytical). The crystal faces were indexed on a
SMART 1000/APEX II single crystal diffractometer (Bruker Corp.).
Electron micrograph images were collected using a JSM-6700F field
emission scanning electron microscope (JEOL Ltd.). Thermal
stability measurements were collected on a Pyris Diamond TG/
DTA (Perkin-Elmer Instruments) between 23 and 1000 °C with a
heating rate of 10 °C/min. For indentation measurements, the
samples were encased in a slow-curing epoxy resin and preliminary
polishing was carried out using silicon carbide abrasive paper.
Diamond films (30, 15, 6, 3, and 1 µm particle sizes) were used
for fine polishing in order to obtain a mirror finish. Microindentation
experiments were performed on a Vickers diamond microindenter
Powder X-ray diffraction was also collected on the as-grown
crystals oriented such that the hexagonal faces were parallel to
the horizontal plane of the diffractometer in order to confirm
that the crystals grow along the c-axis. Figure 2B shows the
X-ray pattern for the as-grown crystal. Only three peaks are
present, corresponding to the (002), (004), and (006) planes,
demonstrating that the (00l) plane grows outward. This growth
pattern leads to the formation of hexagonal platelets oriented
perpendicularly to the c-axis. Attempts to refine the unit cell
using single crystal diffraction were unsuccessful because of
the large degree of twinning present in the crystals (observed
in Figure 1A), which are most likely due to 60° rotations in the
ab plane during the growth process. However, the terminating
crystallographic planes present on the surface of the crystals as
shown in Figure 3 provide further evidence that the crystals
(
Buehler Ltd.). Fifteen indents were made with a Vickers indenter
at each load, beginning with 4.9 N and ending at 0.49 N, to ascertain
the load-dependent hardness. The indentation diagonal lengths were
measured using an Axiotech 100 reflected-light microscope (Carl
Zeiss, Inc.) under 500× magnification. Digital images were taken
using an attached AxioCam MRc color CCD camera (Carl Zeiss).
Nanoindentation was performed using a Nano Indenter XP with a
Berkovich diamond indenter (MTS Systems Corp.). Hardness values
were calculated in situ according to the method developed by Oliver
2
grow along the c-axis. Previously, ReB synthesized in an optical
2
0
and Pharr.
floating zone (FZ) furnace was reported to grow in the (00l)
Electrical resistivity measurements were performed on a polished
crystal 800 µm × 1600 µm × 700 µm using a standard four-probe
configuration. The probes were attached to the (002) face and data
were collected upon heating from 12.5 to 300 K. Magnetic
susceptibility measurements were made using a Magnetic Properties
Measurement System (Quantum Design, Inc.) in a direct current
field from 2 to 300 K.
19
direction, in agreement with our own observations.
Chemical Analysis. Chemical analysis was performed using
inductively coupled plasma atomic emission spectroscopy (ICP-
AES). The nominal composition of ReB was determined to
2
have a true composition of ReB1.85. This value is in good
agreement with the reported analytically determined value of
2
1
2
WB1.85 for “WB ” crystals grown in an aluminum flux. The
Results and Discussion
boron-deficient composition of the diboride crystals provides
confirmation for the defective nature of the puckered boron
Structure Analysis. Crystals obtained from the aluminum flux
have well-defined hexagonal symmetry, and the largest crystals
grow to a maximum size of 3 mm in diameter and 1 mm thickness
7
,22,23
layers that exist in both compounds.
The composition of
arc-melted ReB was analyzed as a control and determined to
2
(Figure 1). The hexagonal faces, clearly visible in Figure 1A,
form in a 1:2 ratio. ReB crystals grown in the FZ furnace were
2
indicate that the crystals grow primarily along the c-axis. The
crystal growth does not go to completion, as indicated by the
also shown to be of stoichiometric composition, as determined
1
9
by ICP-AES. The boron-deficient nature of our ReB crystals
2
presence of ReB
Powder diffraction measurements were taken on pulverized
ReB crystals and indexed, using silicon (Cerac, 99.999%) as
an internal standard. The powder pattern was matched to JCPDS
file 00-011-0581, confirming the growth of ReB crystals (Figure
2
powder along with the formed crystals.
is then a direct result of growing the crystals in a metal flux
and may be responsible for the lower hardness values discussed
below.
2
(
21) Okada, S.; Kudou, K.; Lundstrom, T. Jpn. J. Appl. Phys., Part 1 1995,
4, 226–31.
22) Lundstr o¨ m, T. Acta Chem. Scand. 1968, 22, 2191–2199.
2
3
(
(
20) Oliver, W. C.; Pharr, G. M. J. Mater. Res. 1992, 7, 1564.
(23) McColm, I. J. Ceramic Hardness; Plenum Press: New York, 1990.
1
6954 J. AM. CHEM. SOC. 9 VOL. 130, NO. 50, 2008

Metallic, Superhard Rhenium Diboride Crystals
A R T I C L E S
Figure 2. (A) Powder diffraction pattern of crushed ReB
2
crystals. The pattern is indexed according to JCPDS 00-011-0581. (B) Powder X-ray diffraction
pattern of an as-grown ReB
the crystal.
2
crystal oriented with respect to the c-axis. The large amorphous envelope at 2θ ) 20° is attributed to the epoxy resin encasing
where d is the indentation length of the diagonal (mm), P is
2
the applied load (kg), and H
V
is the Vickers hardness (kg/mm ).
The constant φ is a geometric factor dependent on the specific
indenter geometry in order to allow conversion of the measured
diagonal into contact area, and it has a value of 1.8544 for a
Vickers indenter. More recently, hardness values have begun
2
to be reported in gigapascals (GPa). To convert from kg/mm
to GPa, the values obtained from eq 1 must be multiplied by a
factor of 0.009807. Microindentation results for the ReB
crystals are shown in Figure 4. Indentations were made on the
002) plane and the plane perpendicular to the c-axis in order
2
(
to determine the hardness anisotropy. Indexing of the direction
cut perpendicular to the basal plane by single crystal diffraction
was inconclusive; however, because the angle between these
two planes was measured to be 90°, this plane will be referred
to as (hk0). Both lattice planes exhibit the phenomenon of load-
dependent hardness, known as the indentation size effect (ISE).
This effect was previously observed in polycrystalline ingots
Figure 3. Schematic of the terminating crystallographic planes on a flux-
grown ReB crystal determined using single crystal diffraction.
2
Further elemental analysis indicated that no oxygen was
present in the crystals (0.000%). However, aluminum inclusions
comprised 1.1 atom % of the metal concentration, resulting in
of ReB and is commonly attributed to strain gradient plasticity
2
an actual composition of ReAl0.011
B1.85, although what sites the
9
under the indenter. Under low load, the (002) plane exhibits a
aluminum atoms occupy in the lattice is not known. This is to
be expected when synthesizing crystals via the flux method,
especially when using molten metals. The inclusion of flux into
the crystal lattice has been previously reported for various other
maximum hardness value of 40.5 ( 2.4 GPa, approximately
6
% higher than the hardness of the (hk0) plane. This value
steadily decreases, reaching a minimum hardness under the
maximum applied load, 4.9 N, at which point the values for
both lattice planes converge to a hardness of ∼28 GPa. The
reason the two different planes exhibit anisotropic behavior
exclusively under low load is likely due to the masking of the
primary slip system at high load. At higher indentation test
forces, plastic flow occurs on multiple slip systems in order to
compensate for the increase in deformed volume under the
2
1,24,25
boride syntheses.
Hardness. Vickers hardness was determined by taking the
average value for the diagonals of the residual indentation and
solving for hardness according to eq 1:
2
6
P
H ) φ
(1)
V
2
d
(
25) Nakano, K.; Hayashi, H.; Imura, T. J. Cryst. Growth 1974, 24, 679–
(
24) Higashi, I.; Takahashi, Y.; Atoda, T. J. Cryst. Growth 1976, 33, 207–
11.
682.
2
(26) Aguilar-Santillan, J. Acta Mater. 2008, 56, 2476–2487.
J. AM. CHEM. SOC. 9 VOL. 130, NO. 50, 2008 16955

A R T I C L E S
Levine et al.
18
2
plane of flux-grown ReB under an equivalent load. Part of the
decrease in hardness can be attributed to the boron-deficient
structure of the flux-grown crystals. Additionally, the smaller lattice
parameters presented above suggest a higher vacancy of boron
9
atoms compared to arc-melted ReB
7
2
2
(a ) 2.900, c ) 7.478). A
.25% reduction in the number of boron atoms in the crystal (1.85/
.00) would reduce the extent of covalent bonding between the
rhenium and boron atoms (the reason for the higher hardness of
15
2
ReB relative to other materials) and lower the measured hardness
values. Furthermore, single crystals tend to have lower hardness
than polycrystalline samples because of the lack of grain bound-
aries, which serve to inhibit crack propagation and therefore
28,29
increase hardness.
In our previous work, we predicted that the (002) plane should
be the hardest crystallographic direction in ReB because of the
2
layered nature of the compound and the covalent bonding of Re
9
Figure 4. Vickers hardness for the (002) plane (blue circles) and the (hk0)
and B atoms between layers. This hypothesis was supported by
plane (red triangles) of ReB
with decreasing load, reaching a maximum of 40.5 GPa for the (002) plane
under a load of 0.49 N.
2
flux-grown crystals. The hardness increases
evidence from preliminary hardness data and electron backscat-
tering diffraction, indicating a trend toward increased hardness
along the direction oriented perpendicular to the c-axis. Addition-
ally, incompressibility data and lattice-dependent high-pressure
radial diffraction experiments indicated that the c-axis compresses
the least under hydrostatic stress and supports the greatest degree
9
of shear stress, respectively. The results presented here confirm
that the (002) plane is, in fact, the hardest direction.
Hardness anisotropy as a function of crystallographic direction
has been reported in the literature for various other diborides.
Studies on crystals of IVa, Va, and VIa transition metal diborides
synthesized by both flux and FZ methods reveal that anisotropy in
hardness measurements is related to crystal morphology and
3
0-32
orientation during growth.
temperature exhibited the highest hardness. For example, FZ
2
crystals of TiB and VB , both of which have hexagonal AlB -
The largest crystal planes at a given
2
2
type structures, were observed to be harder in the c-plane (00l)
direction compared to the a-plane (100) direction and grew along
the c-axis. Similar results were found for ZrB
The data for ReB flux crystals coincide with these observations
and confirm that the (002) plane is the hardest plane in ReB
2 2
and HfB crystals.
2
Figure 5. Load vs displacement data collected using a Berkovich diamond
nanoindenter for the (002) plane (solid circles) and the (hk0) plane (open
2
.
triangles) of flux-grown ReB
penetrates deeper into the (hk0) plane, indicative of a lower hardness for
that direction.
2
crystals. For a given load, the diamond tip
Indentation Modulus. The higher hardness of (002) compared
to (hk0) is expected to be related to the anisotropy of the
Young’s moduli of specific crystallographic directions. To
confirm this theory, the nanoindentation data have also been
used to calculate elastic moduli. Due to the lack of an
experimentally determined Poisson’s ratio, the theoretically
indenter. The presence of multiple slip mechanisms masks the
hardness anisotropy characteristic of only one active slip system,
which differs for each lattice plane under low load.
1
5
2
calculated value of υ ) 0.18 was used for ReB in addition
Nanoindentation data are reported in Figure 5 for ReB
2
to the standard values of υ ) 0.07 and E ) 1140 GPa for
crystals. The reported values were obtained from penetration
of the Berkovich diamond nanoindenter 200-800 nm beneath
the specimen surface. Once again, indentation experiments were
performed on the two sets of perpendicular planes: (002) and
2
0
diamond, as described previously by Oliver and Pharr. An
indentation modulus of 675 ( 7 GPa for the basal plane of
ReB was calculated over the defined range of 200-800 nm;
2
the corresponding value for the perpendicular plane is 510 (
3 GPa. The anisotropy present in the indentation moduli is
(
hk0). The hardness measured along (002) is 36.4 ( 0.2 GPa,
1
while the hardness of the (hk0) plane is 7% smaller with a value
of 34.0 ( 1.3 GPa. The difference in hardness between
perpendicular planes for the nanoindentation data is in good
agreement with the Vickers microindentation anisotropy reported
above.
consistent with both the nano- and microindentation hardness
values, with the c-axis possessing a higher hardness and greater
indentation modulus than the (hk0) plane.
Determination of the elastic moduli by nanoindentation is
based on the theory of contact mechanics for elastically isotropic
Note that the low load micro- and nanohardness data reported
9,27
2
here are lower than the values reported for arc-melted ReB
5% and 2%, respectively. Similarly, Lyashchenko et al. reported
a Vickers hardness of 37.2 GPa under a load of 0.98 N for zone-
melted ReB compared to the 36.2 GPa obtained here for the (002)
by
1
(
28) Hall, E. O. Proc. Phys. Soc. London, Sect. B 1951, 64, 747–753.
(29) Petch, N. J. J. Iron Steel Res. Inst. 1953, 174, 25–28.
(
(
30) Otani, S. J. Ceram. Soc. Jpn. 2000, 108, 955–956.
2
31) Otani, S.; Korsukova, M. M.; Mitsuhashi, T. J. Cryst. Growth 1998,
1
94, 430–433.
(
27) Chung, H.-Y.; Weinberger, M. B.; Yang, J.-M.; Tolbert, S. H.; Kaner,
(32) Otani, S.; Xuan, Y.; Yajima, Y.; Mori, T. J. Alloys Compd. 2003,
R. B. Appl. Phys. Lett. 2008, 92, 261904.
361, L1–L3.
1
6956 J. AM. CHEM. SOC. 9 VOL. 130, NO. 50, 2008

Metallic, Superhard Rhenium Diboride Crystals
A R T I C L E S
2
0,33
materials.
here are expected to differ from the Young’s modulus because
of the anisotropy inherent in the layered lattice of ReB . The
Consequently, the indentation moduli calculated
2
Young’s modulus in the direction of the indentation will
dominate the elastic response; however, the indentation modulus
33
will also be partially dependent on the other elastic constants.
Thus, the elastic anisotropy present in ReB crystals measured
by nanoindentation can be reconciled with the elastic constants
2
1
5
determined by first-principle calculations. The calculated
elastic stiffness constants, C11 and C33, which are also highly
anisotropic, measure the resistance to linear compression along
the a and c-axes, respectively. The constant for the c-axis, C33
,
has the largest value (approximately 1100 GPa), which explains
the higher indentation modulus along this direction.
The elastic moduli differ by 25% compared to only 6% for
the hardness values for (002) and (hk0). This difference in
anisotropy can also be explained by careful manipulation of
the elastic constants. Hao et al. calculated the ratio of the linear
compressibility coefficients for the c and a-directions:
15
Figure 6. Resistivity vs temperature for a ReB crystal measured along
the (002) plane. ReB exhibits metallic conductivity with a room temperature
2
resistivity of Fab (300) ) 40.7 µΩ·cm and a residual resistivity ratio ) 13.
2
k /k )(C + C - 2C )/(C - C )
(2)
c
a
11
12
13
33
13
Table 1. Electrical Resistivity and Vickers Hardness Values for
which is indicative of the degree of compressional anisotropy,
Various Hard and Superhard Compounds
34
with unity indicating an isotropic material. Similarly, the shear
3
4
a
anisotropy ratio can be calculated according to eq 3:
compd
resistivity at 300 K, Fab (µΩ·cm)
Vickers hardness (GPa)
b
b
ReB
2
40.7
40.5
A)2C /(C - C )
(3)
2 c a
ReB has values of k /k ) 0.56 and A ) 1.06. These numbers
c
d
d
d
d
f
4
4
11
12
TiB2
HfC
WC
28.4
33.3
28.1
23.5
23.5
20.6
c
109
c
53
indicate that elastic compression is more anisotropic than shear.
Numerous studies have shown that hardness is more highly
e
4
B C
760000
c
TiN
21.7
3
5-38
correlated with shear strength than compressive strength.
a
Therefore, we expect hardness to be more isotropic than the
elastic modulus, which is observed experimentally. The greater
degree of anisotropy present for indentation moduli compared
to hardness indicates different mechanics giving rise to elastic
and plastic deformation and suggests that mechanical anisotropy
is reduced in the presence of plastic deformation.
4
Hardness values are reported under a load of 50 gf; load for B C
b c
not reported. This work. Schwarzkopf, P.; Kieffer, R. Refractory
Hard Metals; Macmillan Company: New York, 1953. Shackelford,
d
J. F., Alexander, W., Eds.; CRC Materials Science and Engineering
e
Handbook, 3rd ed.; Boca Raton, FL, 2001. Meerson, G. A.; Kiparisov,
S. S.; Gurevich, M. A.; Feng-Siang, D. Poroshk. Metall. 1965, 27,
f
6
2-68. Reference 23.
Electrical Resistivity. In-plane electrical resistivity (Fab
measurements performed on ReB crystals are shown in Figure
, and electrical resistivity values for various other hard materials
are listed in Table 1 for comparison. ReB exhibits metallic
)
3
9
K, in accordance with the findings of Kawano et al. ReB
2
2
6
crystals are paramagnetic with a Curie-tail at low temperatures.
Thermal Stability. Thermogravimetric data are presented in
2
conductivity, as its conductivity increases with decreasing
temperature. A room temperature resistivity of Fab(300K) ) 45
Figure 7 for a flux-grown ReB
14.5 mg of ReB (nominal composition) powder synthesized
via an elemental solid-state reaction. Upon heating in dry air,
the ReB powder exhibits a very slight drop in mass at 100 °C,
corresponding to the loss of absorbed water. At 600 °C, a large
exothermic peak presents itself in the DTA curve as the powder
begins to lose a significant portion of its mass. The mass loss
continues until the completion of the run, totaling over 50% of
the original sample mass. Due to the fact that boron comprises
2
crystal weighing 21.95 mg and
2
(
15 µΩ·cm was measured, and impurity scattering accounts
for a residual resistivity of Fab(0) ) 3.5(1) µΩ·cm and a residual
2
resistivity ratio of 13. These results are consistent with the recent
theoretical calculations predicting that ReB
2
is metallic with a
nonzero density of states at the Fermi level due to overlap of
1
5
the 2p orbitals of B with the 5d orbitals of Re. To the best of
the authors’ knowledge, ReB is the hardest bulk material
2
possessing metallic conductivity, with a Vickers hardness
considerably higher than those of any of the other materials
present in Table 1.
Magnetic Susceptibility. Magnetic susceptibility measure-
ments confirm the absence of superconductivity down to 2.0
only 10 mass % of ReB
primarily to the loss of rhenium by the formation of volatile
ReO plus some loss of boron by the formation of B . Initially,
the ReB crystal responds similarly to heating in air, with a
small drop in mass at 100 °C. However, no further change is
observed until approximately 800 °C, when the crystal loses a
small percentage of mass. Note that if the flux crystal is heated
at a slower rate (2 °C/min) up to 1000 °C, the mass loss
increases accordingly, totaling 1.5% of the original sample
weight.
2
, the change in weight can be attributed
3
2 3
O
2
(
(
33) Hay, J. C.; Sun, E. Y.; Pharr, G. M.; Becher, P. F.; Alexander, K. B.
J. Am. Ceram. Soc. 1998, 81, 2661–2669.
34) Steinle-Neumann, G.; Stixrude, L.; Cohen, R. E. Phys. ReV. B 1999,
6
0, 791.
(
(
35) Teter, D. M. MRS Bull. 1998, 23, 22.
36) Brazhkin, V. V.; Lyapin, A. G.; Hemley, R. J. Philos. Mag. A 2001,
Visual inspection of the crystal after heating indicates the
presence of a glassy coating. Sonication in methanol removed
8
2, 231.
(
(
37) Leger, J. M.; Djemia, P.; Ganot, F.; Haines, J.; Pereira, A. S.; da
Jornada, J. A. H. Appl. Phys. Lett. 2001, 79, 2169.
38) Gilman, J. J.; Cumberland, R. W.; Kaner, R. B. Int. J. Refract. Met.
Hard Mater. 2006, 24, 1–5.
(39) Kawano, A.; Mizuta, Y.; Takagiwa, H.; Muranaka, T.; Akimitsu, J.
J. Phys. Soc. Jpn. 2003, 72, 1724–1728.
J. AM. CHEM. SOC. 9 VOL. 130, NO. 50, 2008 16957

A R T I C L E S
Levine et al.
oriented along the c-axis and exhibit directional anisotropy.
Indentation measurements of the (002) and (hk0) planes of ReB
2
show that the (002) plane is the hardest crystallographic plane,
with the highest indentation modulus. Thermogravimetric
analysis indicated enhanced thermal stability of ReB crystals
2
up to 1000 °C. Resistivity measurements demonstrated that ReB
2
is a conducting material.
ReB is the only bulk superhard material so far to exhibit
2
metallic behavior. Most superhard materials are insulators
because of the large band gap that results from strong covalent
bonding and filling of the bonding orbitals, while leaving the
antibonding orbitals unoccupied. The band gaps for diamond
and cubic boron nitride are E
respectively, compared to 0 eV for ReB
ReB crystals to thermal degradation and their ability to freely
conduct electricity paves the way for development of superhard
coatings with technical capabilities for use in the defense and
aerospace industries.
g
) 5.4 eV and E
g
) 6.4 eV,
4
1,42
2
.
The resistance of
2
Figure 7. Thermogravimetric data for ReB
2
powder (blue lines) and a ReB
2
crystal (red lines). The crystal loses a negligible amount of mass (solid
line) compared to the case of the powder, which undergoes rapid
decomposition at 600 °C, as indicated by the weight loss and large
exothermic peak in the DTA curve (dashed lines).
Acknowledgment. The authors would like to thank Dr. E. Sung
for use of the microindenter, Dr. Saeed Khan for crystal structure
determination, Dr. Amir Liba for chemical analysis, and Dr.
Danielle Gray (Northwestern University) for help with the Rietveld
refinement. This work was funded by the National Science
Foundation under Grants DMR-0453121 (R.B.K.), DMR-0805357
(R.B.K.), and DMR-0520552 (S.E.B.) and an Integrative Graduate
Education and Research Traineeship (J.B.L., J.A.W.).
the layer and restored the crystal to its previously lustrous
appearance. The enhanced stability of the ReB crystal is likely
2
due to the leaching out of boron from the lattice. The boron
then reacts with atmospheric oxygen to form a protective surface
coating of B
lowers the rate at which any further oxidation might occur. The
thermal response of ReB is contrasted with the behavior of
2 3 2 3
O (B O is soluble in methanol) that drastically
2
other borides that tend to form stable transition metal oxides
upon heating, resulting in weight gains ranging from a few
JA804989Q
2
1,40
percent (WB
Conclusions
We have reported the synthesis of superhard ReB
2 2
) to an excess of 20% (TaB ).
(
40) Okada, S.; Kudou, K.; Higashi, I.; Lundstroem, T. J. Cryst. Growth
993, 128, 1120–4.
41) CRC Handbook of Chemistry and Physics, 88th ed.; CRC: 2007-
008.
(42) Chrenko, R. M. Solid State Commun. 1974, 14, 511–515.
1
(
2
crystals
by a flux method using molten aluminum. The crystals grow
2
1
6958 J. AM. CHEM. SOC. 9 VOL. 130, NO. 50, 2008