28. T. J. Drye, M. E. Cates, J. Chem. Phys. 96, 1367 (1992).
29. P. Panizza, G. Cristobal, J. Curtly, J. Phys. Cond. Matter
10, 11659 (1998).
30. A. Bernheim-Groswasser, E. Wachtel, Y. Talmon,
Langmuir 16, 4131 (2000).
31. T. Tlusty, S. A. Safran, J. Phys. Cond. Matter 12, A253
(2000).
32. This research program was supported by the NSF-
sponsored Materials Science and Engineering Cen-
ter (MRSEC) at the University of Minnesota and by
the NIH (1R21EB00989-01). D. Morse engaged the
authors in enlightening discussions.
8 January 2003; accepted 11 March 2003
Multifunctional Alloys Obtained
via a Dislocation-Free Plastic
Deformation Mechanism
Takashi Saito,
1
* Tadahiko Furuta,
1
Jung-Hwan Hwang,
1
Shigeru Kuramoto,
1
Kazuaki Nishino,
1
Nobuaki Suzuki,
1
Rong Chen,
1
Akira Yamada,
1
Kazuhiko Ito,
1
Yoshiki Seno,
1
Takamasa Nonaka,
1
Hideaki Ikehata,
1
Naoyuki Nagasako,
1
Chihiro Iwamoto,
2
Yuuichi Ikuhara,
2
Taketo Sakuma
3
We describe a group of alloys that exhibit “super” properties, such as ultralow
elastic modulus, ultrahigh strength, super elasticity, and super plasticity, at
room temperature and that show Elinvar and Invar behavior. These “super”
properties are attributable to a dislocation-free plastic deformation mecha-
nism. In cold-worked alloys, this mechanism forms elastic strain fields of
hierarchical structure that range in size from the nanometer scale to several
tens of micrometers. The resultant elastic strain energy leads to a number of
enhanced material properties.
Mechanical properties, such as strength, of
metallic materials are strongly affected by
metallurgical processes such as heat treat-
ment and plastic working, which bring
modifications in the microstructure. On the
other hand, these processes have no sub-
stantial effect on physical properties such
as elastic modulus and thermal expansion.
The reason for this is that the changes that
can be affected by plastic working and heat
treatment do not extend to interatomic
bonds or electronic states.
We present a group of alloys that exhibit
multiple “super” properties and drastic changes
in physical properties after plastic working at
room temperature. These alloys simultaneously
offer super elasticity, super strength, super cold-
workability, and Invar and Elinvar properties.
The alloys consist of Group IVa and Va ele-
ments and oxygen and share the following three
electronic magic numbers: (i) a compositional
average valence electron number [electron/at-
om (e/a) ratio] of about 4.24; (ii) a bond order
(Bo value) of about 2.87 based on the DV-X␣
cluster method, which represents the bonding
strength (1–3); and (iii) a “d” electron-orbital
energy level (Md value) of about 2.45 eV,
representing electronegativity. The properties
emerge only when all three of these magic
numbers are satisfied simultaneously. Various
alloy composition combinations meet these cri-
teria, such as Ti-12Ta-9Nb-3V-6Zr-O and Ti-
23Nb-0.7Ta-2Zr-O [mole percent (mol %)],
wherein each alloy has a simple body-centered
cubic (bcc) crystal structure. In order to exhibit
these properties, each alloy system requires
substantial cold working and the presence of a
certain amount of oxygen, restricted to an oxy-
gen concentration of 0.7 to 3.0 mol %.
Typical properties of the alloys are shown in
Fig. 1 for samples before and after cold swag-
ing with 90% reduction in area (4 ). Tensile
stress-strain curves shown in Fig. 1A indicate
that cold working substantially decreases the
elastic modulus and increases the yield strength
and confirm nonlinearity in the elastic range,
with the gradient of each curve decreasing con-
tinuously to about 1/3 its original value near the
elastic limit. As a result of this decrease in
elastic modulus and nonlinearity, elastic de-
formability after cold working reaches 2.5%,
which is at least double the value before cold
working. Generally, large elastic deformations
that occur in so-called “super-elastic alloys” are
known to be reversible martensitic transforma-
tions resulting from deformation, dubbed
“pseudo-elastic deformation” (5, 6). Converse-
ly, the large elastic deformation in the alloy
studied is an intrinsically different “true-elastic
deformation,” which is not accompanied by
phase transformation. The elastic deformability
of the cold-worked material has been found to
increase with decreasing temperature, exceed-
ing 4% at 77 K. The strength of the alloy
increases with decreasing temperature, as in
normal metals, reaching 1800 MPa at 77 K.
Conversely, the elastic modulus of non-cold-
worked samples increases with decreasing tem-
perature, in the same manner as for normal
metals, but, as shown in Fig. 1B, the elastic
modulus of the cold-worked alloy remains
about constant between 77 and 500 K. Elinvar
alloys (7 ), which maintain a constant elastic
modulus over a limited temperature range, have
already been known. However, none of them
has been known to maintain a constant elastic
modulus over such a wide temperature range.
Figure 1C shows the temperature dependence
of linear expansion. In an annealed state, the
alloy exhibits almost linear thermal expansion
behavior similar to that of a normal metal and
continues to expand with increasing tempera-
ture. Its linear expansion coefficient is about
8 ⫻ 10
⫺6
K
⫺1
. For the cold-worked alloy, the
linear expansion coefficient does not exceed
1
Toyota Central Research and Development Labora-
tories, Incorporated, Nagakute Aichi, 480-1192 Japan.
2
Institute of Engineering Innovation, University of
Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656 Japan.
3
Graduate School of Frontier Sciences, University of
Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan.
*To whom correspondence should be addressed. E-
mail: saito@mosk.tytlabs.co.jp
Fig. 1. Comparison of mechanical and physical
properties of developed alloys before and after
cold swaging by 90% reduction in area. (A)
Tensile stress-strain curve for Ti-12Ta-9Nb-
3V-6Zr-1.5O alloy at room temperature, (B)
temperature dependence of Young’s modulus
near zero stress in Ti-23Nb-0.7Ta-2Zr-1.2O
alloy, and (C) temperature dependence of linear expansion in Ti-23Nb-0.7Ta-2Zr-1.2O alloy.
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18 APRIL 2003 VOL 300 SCIENCE www.sciencemag.org464
2 ⫻ 10
⫺6
K
⫺1
over a temperature range of
100 to 500 K but shows a dramatic increase
from about 600 K. The cold-worked alloy
exhibits the Invar property over a wider tem-
perature range than do conventional Invar
alloys (7–9). A similar abnormality in ther-
mal expansion behavior by cold working of
shape memory alloys has recently been re-
ported by Kainuma et al.(10). That phenom-
enon is caused by a reverse transformation of
stress-induced martensite. Conversely, the
abnormality in thermal expansion of the ma-
terial investigated is completely unrelated
to phase transformation. In many cases,
Invar and Elinvar properties have tradition-
ally been attributed to the magnetic mo-
ment of ferromagnetic alloys. However, our
alloy is neither ferromagnetic nor antifer-
romagnetic, but paramagnetic.
The combined properties of the cold-
worked alloy may make it extremely useful.
For example, low elastic modulus and high
strength can make the alloy suitable for ul-
tralightweight springs, and its invariable elas-
tic modulus and thermal expansion properties
may make the alloy an ideal material for
precision instruments for use in rugged envi-
ronments such as in outer space.
The unusual physical properties shown
in Fig. 1 suggest that the plastic deforma-
tion induced by cold working is of a consid-
erably different nature from that of normal
metals. This is supported by the observation
of room-temperature super plasticity such
that no amount of plastic deformation causes
work hardening or a drop in ductility (fig.
S1). Although the cold-worked material has a
trivial uniform tensile elongation as seen in
Fig. 1A, it shows a large local elongation
(reduction in area) and an amazing capacity
for compressive deformation, like that of
clay, by virtue of its strange work-softening
characteristics.
A typical microstructure of Ti-23Nb-
0.7Ta-2Zr-1.2O alloy is shown in Fig. 2. An
optical microstructure comparison of the an-
nealed (Fig. 2A) and the cold-worked (Fig.
2B) materials indicates that the equiaxed beta
grain microstructure of the annealed material
changes into the characteristic “marble-like”
structure after cold working. The marble-like
structure appears to consist of assemblies of
fine filamentary structures. A high-magnifi-
cation transmission electron microscope
(TEM) image of the cold-worked alloy
shows local disturbances (bending) in the
crystal lattice (Fig. 2C). The distribution of
discrete 2- to 3-nm order strain contours is
found to correspond to disturbances in the
crystal lattice. However, observations at dif-
ferent magnifications and orientations re-
vealed virtually no dislocations (fig. S2). In
addition to exhibiting this nanoscale bending,
the crystal lattice was found to bow at a
radius of about 500 nm and at a scale of
several tens of micrometers.
The following model testing was conduct-
ed in order to analyze the plastic deformation
mechanism in detail. A microspecimen of
annealed alloy having a parallel portion about
30 micrometers thick and 150 micrometers
long was subjected to tensile testing under a
microscope. Figure 3, A to D, shows the
changes in the sample surface with the
progress of tensile deformation. The sample
surface exhibited no change through the ini-
tial deformation of about 3%, and subse-
quently a large line pattern suddenly ap-
peared across the parallel portion. The num-
ber of line patterns increased intermittently as
the strain increased. Figure 3E shows TEM
images of thin films prepared with the use of
the focused ion beam method of sections
parallel to the tension direction and perpen-
dicular to the surface of the specimen after
the sample had undergone 10% tensile strain.
The observed structures show that (i) the line
patterns appearing at the sample surface are
each “giant faults” having height differences
of about 300 to 500 nm that appeared within
an extremely short time; (ii) the faults formed
Fig. 2. Comparison of optical microstructure
of Ti-23Nb-0.7Ta-2Zr-1.2O alloy (A) annealed
at 1273 K and (B) cold-worked by 90% reduc-
tion in area. (C) A high-magnification TEM
image of the cold-worked specimen with (110)
normal incident beam using an ultrahigh volt-
age (1.2 MV) TEM. Local disturbances in the
crystal lattice are indicated within open circles.
Fig. 3. (A to D) Changes in surface morphology
of a tensile specimen of annealed Ti-23Nb-
0.7Ta-2Zr-1.2O alloy. The amounts of defor-
mation are (A) 0, (B) 4.3%, (C) 6.1%, and (D)
10.3%. (E) A TEM image near the surface of
the specimen and (F) the corresponding elec-
tron diffraction pattern, which indicates crys-
tal rotation near the giant fault. The foil was
prepared perpendicular to the surface. (G)A
schematic diagram showing orientation near
the giant fault. The {112}⬍111⬎ direction is
one of the slip systems for dislocation glide
and also a major orientation of twinning in bcc
crystals.
R EPORTS
www.sciencemag.org SCIENCE VOL 300 18 APRIL 2003 465
along the plane of maximum shear stress at
about 45° to the tensile direction, not on the
possible bcc crystal slip planes or twin planes
(Fig. 3G); (iii) the grain boundary is greatly
curved near the faults, resulting in large elas-
tic deformation; and (iv) highly distorted and
localized strain fields were generated along
the fault plane (Fig. 3F). This suggests that
the plastic deformation mechanism of this
alloy is an extremely large-scale and discon-
tinuous phenomenon in which the deforma-
tion progresses by formation of giant faults.
Thus, the marbled structure seen in Fig. 2B is
thought to be developed by aggregation of the
“giant faults,” which was highlighted by
chemical etching that reveals the strain field
near the fault. Recrystallized grains nucleate
along the filament structures upon reheating
of the cold-worked material (fig. S3), sup-
porting the view that the line pattern reflects
the elastic strain field.
We examined the effect of cold working and
the role of oxygen with ultrahigh-intense x-ray
diffraction (XRD), electron energy loss spec-
troscopy (EELS) (11), and extended x-ray ab-
sorption fine structure (EXAFS) (12) using an
8-GeV synchrotron radiation beam (13). The
XRD analysis revealed that the material is
essentially composed of bcc phase at the cold-
worked condition and that no phase transforma-
tion such as ␣” martensitic transformation oc-
curs. The EELS analysis on the cold-worked
specimen (Fig. 4A) revealed that the zero-loss
image indicates the strain distribution. The
flecked contrast at a scale of several nanometers
observed in the TEM image was thus found to
represent the elastic strain field distribution. In
addition, the distribution of alloying elements
(in particular zirconium) matches the size of the
strain contours. Figure 4B compares the Fourier
transformed spectra calculated from the K-edge
spectra for niobium and zirconium atoms (EX-
AFS analyses) conducted on six sample types
for determining the oxygen concentration and
the effect of cold working. The niobium atoms
(and tantalum atoms) exhibit about identical
spectra in all six samples, whereas the zirconium
atoms show obvious sample-to-sample differ-
ences. That is, (i) oxygen content and cold
working produce no changes around Group Va
elements, such as niobium and tantalum; (ii)
oxygen atoms tend to build up around the zir-
conium atoms to form atom clusters; (iii) cold
working equalizes the mean distance between
the zirconium atoms and the surrounding first
and second nearest substitutional atoms (mainly
titanium); and (iv) cold working rearranges the
oxygen atoms surrounding zirconium atoms.
Finally, we consider why only alloys of
specific compositions exhibit the curious plastic
deformation behavior. The Young’s modulus of
a Ti-X binary alloy system, comprising titani-
um and a Group Va element X (such as tanta-
lum, niobium, or vanadium), was estimated
from the first principles on the basis of the
ultrasoft pseudopotential method (14, 15) with-
in generalized gradient approximation to the
density function theory (16, 17 ). The calcu-
lation showed an extremely low elastic mod-
ulus at a valence electron number close to
that of the developed alloy (e/a ⫽ 4.24) and
showed that the elastic constants c
11
and c
12
are nearly equal for this composition (fig.
S4). In other words, the Young’s modulus (E)
approaches zero in the bcc crystal ⬍100⬎
direction, and the shear modulus (G) ap-
proaches zero in the ⬍111⬎ direction on the
{011}, {112}, and {123} planes, a typical
slip system in bcc metals (table S1).
Now we can deduce the plastic behavior of
the alloy from the elastic properties described
above. The value of the “ideal shear stress” has
been estimated as about 0.11G
111
(18) for bcc
metals; such values for conventional metals are
several dozen times the actual strength, whereas
that for the developed alloy is estimated to be so
small as to be comparable to the actual strength
by virtue of the peculiar elastic anisotropy de-
scribed above. Although in conventional bcc
metals slip occurs as a result of shear defor-
mation in the ⬍111⬎ closed packed direction
on the {011}, {112}, and {123} slip planes,
elastic deformation occurs readily in the de-
veloped alloy by virtue of its extremely small
G value in this direction. Eventually, when
local stresses reach their critical value (ideal
shear stress) (18), shear deformation pro-
ceeds along the maximum shear stress plane
without the aid of any dislocations. Here we
should recall that the abnormal plastic defor-
mation behavior of a Ti-X alloy of about a
specific composition only appears upon ad-
dition of a certain amount of zirconium and
oxygen. It may be possible that the Zr-O atom
clusters, which distributed densely over an
extremely short range, could effectively in-
hibit dislocation activity.
As a result, dislocation-free plastic deforma-
tion can be realized, and the “giant fault” visible
in Fig. 3E dominates the plastic deformation.
Such plastic deformation mechanisms unac-
companied by dislocation activity are thought
to be the reason why huge plastic deformation
is possible, as in the case of clay, and why no
work hardening is exhibited. The formation of
Fig. 4. (A) A distribution of alloying elements in the 90% cold-worked Ti-23Nb-0.7Ta-2Zr-1.2O alloy by
EELS using a 200-kV TEM and a TEM image of the same magnification. (B) Comparison of the Fourier
transferred spectra calculated from the K-edge EXAFS spectra for niobium and zirconium atoms using
8-GeV synchrotron radiation beam obtained for six sample types. Specimens of three oxygen levels of
0.5, 1.2, and 2.5 mol % were examined before and after 90% cold swaging. Ti
n
and O
n
represent
positions of neighboring titanium and interstitial oxygen atoms, respectively. Strong dependences on
both oxygen concentration and cold working are seen only for zirconium atoms, whereas the spectra
around niobium atoms (same for tantalum atoms) are almost overlapping for all specimens.
R EPORTS
18 APRIL 2003 VOL 300 SCIENCE www.sciencemag.org466
“giant faults” does not lead to total failure,
because the displacement equivalent to the fault
formation is complemented by elastic deforma-
tions around the fault as seen in Fig. 3F. There-
fore, as plastic working proceeds, elastic strain
energy is accumulated. The accumulation of the
elastic strain energy is accompanied by the
coordinated displacement of the zirconium and
oxygen atoms as shown in Fig. 4. The nanom-
eter-scale bending is discrete and accumulates
into large crystal curvatures of a scale of several
tens of micrometers, which indicate that the
large elastic strain energy is accumulated dis-
cretely and hierarchically in the alloy. We con-
ceive, for the time being, that all the dramatic
changes in physical properties by cold working
seen in Fig. 1 are attributed to this accumulated
nanoscale discrete elastic strain energy.
References and Notes
1. J. C. Slater, The Calculation of Molecular Orbitals
( Wiley, New York, 1979).
2. F. W. Averill, D. E. Ellis, J. Chem. Phys. 59, 6412
(1973).
3. M. Morinaga, N. Yukawa, T. Maya, K. Sone, H. Adachi,
in Sixth World Conference on Titanium, Societe´ Fran-
c¸aise de Metallurgie et des Materiaux, Cannes, France,
6 to 9 June 1988, P. Lacombe, R. Tricot, G. Beranger,
Eds. (Les Editions de Physique, Les Ulis Cedex, France,
1989), pp. 1373–1379.
4. Materials and methods are available as supporting
material on Science Online.
5. T. W. Duerig, A. R. Pelton, in Materials Properties
Handbook: Titanium Alloys, R. Boyer, G. Welsch, E. W.
Collings, Eds. (American Society for Metals Interna-
tional, Materials Park, OH, 1994), pp. 1035–1048.
6. C. Baker, Metal Sci. J. 5, 92 (1971).
7. Y. Nakamura, IEEE Trans. Magn. 12, 278 (1976).
8. E. P. Wohlfarth, IEEE Trans. Magn. 11, 1638 (1975).
9. C. E. Guillaume, Proc. Phys. Soc. London 32, 374
(1920).
10. R. Kainuma, J. J. Wang, T. Omori, Y. Sutou, K. Ishida,
Appl. Phys. Lett. 80, 4348 (2002).
11. R. F. Egerton, Electron Energy-Loss Spectroscopy in
the Electron Microscope (Plenum, New York, 1986).
12. B. K. Teo, EXAFS: Basic Principles and Data Analysis
(Springer-Verlag, Berlin, 1986).
13. H. Kitamura, J. Synchrotron Radiat. 5, 184 (1998).
14. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990).
15. K. Laasonen, A. Pasquarello, R. Car, C. Lee, D. Vander-
bilt, Phys. Rev. B 47, 10142 (1993).
16. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).
17. W. Kohn, L. J. Sham, Phys. Rev. 140, A1133 (1965).
18. C. R. Krenn, D. Roundy, J. W. Morris Jr., M. L. Cohen,
Mater. Sci. Eng. A 319 –321, 111 (2001).
Supporting Online Material
www.sciencemag.org/cgi/content/full/300/5618/464/
DC1
Materials and Methods
Figs. S1 to S4
Table S1
30 December 2002; accepted 4 March 2003
Packing C
60
in Boron Nitride
Nanotubes
W. Mickelson, S. Aloni, Wei-Qiang Han, John Cumings, A. Zettl*
We have created insulated C
60
nanowire by packing C
60
molecules into the
interior of insulating boron nitride nanotubes (BNNTs). For small-diameter
BNNTs, the wire consists of a linear chain of C
60
molecules. With increasing
BNNT inner diameter, unusual C
60
stacking configurations are obtained (in-
cluding helical, hollow core, and incommensurate) that are unknown for bulk
or thin-film forms of C
60
.C
60
in BNNTs thus presents a model system for
studying the properties of dimensionally constrained “silo” crystal structures.
For the linear-chain case, we have fused the C
60
molecules to form a single-
walled carbon nanotube inside the insulating BNNT.
Crystal structure is key in determining the
mechanical, electronic, thermal, and magnet-
ic properties of materials. Silicon, for exam-
ple, is a modest bandgap semiconductor in its
common diamond structure, but in its high-
pressure simple hexagonal structure it is a
metal and a superconductor (1). In low-
dimensional nanostructures, crystal structure
conspires with additional quantum mechani-
cal confinement and surface effects to dictate
the (often unusual) material properties. Of
current interest is the ability to reliably ma-
nipulate atomic or molecular species into dif-
ferent nanoscale configurations, in which the
crystal structure is dictated not only by inter-
atomic or intermolecular interactions but also
by self-imposed surface energy terms (such
as in suspended metal nanowires) (2, 3)or
externally applied geometrical constraints
[(with examples ranging from liquids freez-
ing in confined geometries (4 ) to atoms as-
sembled on surfaces (5)]. Because of its high
symmetry and relatively weak intermolecular
interactions, the fullerene C
60
presents a near-
ideal system for studying different crystal
structures possible in a weakly interacting,
dimensionally constrained system.
We here report unusual nanowire crystal
structures of C
60
obtained by packing the
spherical fullerene molecules into the interior
spaces of boron nitride nanotubes (BNNTs).
BNNTs (6–10) have an energy gap of 5 eV
independent of wall number, diameter, or
chirality and thus constitute desirable insulat-
ing structures for geometrically and electron-
ically confining atomic, molecular, or nano-
crystalline species. We find that filling small-
diameter BNNTs results in a linear chain of
C
60
molecules, analogous to previously ob-
served carbon nanotube “peapods” (11), but
with a significantly smaller C
60
-C
60
intermo-
lecular distance. With increasing BNNT in-
ner diameter, new stacking configurations are
obtained that are unknown for bulk or thin-
film forms of C
60
. Our results are well ac-
counted for by a simple geometrical model of
hard spheres packed within a cylindrical cav-
ity. Through postsynthesis treatment, it is
possible to fuse the C
60
molecules together
into carbon nanotubes, yielding as a final
product single-walled carbon nanotubes indi-
vidually sheathed within electrically insulat-
ing BNNTs.
Pure BNNTs were first synthesized with
either a plasma-arc discharge method (9),
yielding primarily double-walled BNNTs, or
a carbon-nanotube substitution reaction (10),
yielding multiwalled BNNTs. The as-synthe-
sized nanotube-rich soot was heat treated in
air at 800°C for 20 min to remove excess
boron nanoparticles and to open the tips of
the BNNTs. The gray, heat-treated tubes
were then sealed in an evacuated (10
– 6
torr)
quartz ampoule together with commercially
obtained C
60
powder (MER Corp., Tucson,
Arizona, 99.5%) in about a 5 :1 C
60
:BNNT
mass ratio and uniformly heated to between
550° and 630°C for 24 to 48 hours. The
ampoules were broken open, and the resultant
black material was sonicated in either isopro-
panol or chloroform and deposited onto
lacey-carbon grids for transmission electron
microscope (TEM) characterization, with
TOPCON 002B, Phillips CM200, and JEOL
2011 microscopes operating at electron ener-
gies typically near 100 keV.
Figure 1 shows TEM images of BNNTs
treated with C
60
. In Fig. 1A, two double-
walled BNNTs are shown. The upper of the
two tubes in Fig. 1A has an inner diameter
of ⬃1.3 nm. The interior of this tube is well
resolved and shows a linear chain of nearly
evenly spaced C
60
molecules. This hybrid
structure is very similar in appearance to
previously reported (11) single-walled car-
bon nanotube/C
60
peapods. The lower
BNNT in Fig. 1A is partially filled with
amorphous boron nitride; this filling has
substantially prevented C
60
infiltration.
Figure 1B shows additional TEM images of
BNNTs treated with C
60
. The lower half of
the figure shows a five-walled BNNT with
innermost diameter of 1.3 nm, which is
efficiently filled with a linear chain of C
60
.
Department of Physics, University of California at
Berkeley, Berkeley, CA 94720, USA. Materials Sciences
Division, Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA.
*To whom correspondence should be addressed. E-
mail: azettl@socrates.berkeley.edu
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www.sciencemag.org SCIENCE VOL 300 18 APRIL 2003 467
