X-ray diffraction measurements were performed on nanocrystalline iron up to 46 GPa. For nanocrystalline epsilon-Fe, analysis of lattice parameter data provides a bulk modulus, K, of 179±8 GPa and a pressure derivative of the bulk modulus, K[prime], of 3.6±0.7, similar to the large-grained control sample. The extrapolated zero-pressure unit cell volume of nanocrystalline epsilon-Fe is 22.9±0.2 Å^3, compared to 22.3±0.2 Å^3 for large-grained epsilon-Fe. No significant grain growth was observed to occur under pressure

Chen, B.

Fultz, B.

Kruger, M. B.

Penwell, D.

Yue, A. F.

English

Caltech Authors - Main

JOURNAL OF APPLIED PHYSICS VOLUME 89, NUMBER 9 1 MAY 2001Nanocrystalline iron at high pressure
B. Chen,a) D. Penwell, and M. B. Kruger
Department of Physics, University of Missouri, Kansas City, Missouri 64110
A. F. Yue and B. Fultz
Department of Engineering and Applied Science, California Institute of Technology, Pasadena,
California 91125
~Received 4 January 2001; accepted for publication 29 January 2001!
X-ray diffraction measurements were performed on nanocrystalline iron up to 46 GPa. For
nanocrystalline e-Fe, analysis of lattice parameter data provides a bulk modulus, K, of 179
68 GPa and a pressure derivative of the bulk modulus, K8, of 3.660.7, similar to the large-grained
control sample. The extrapolated zero-pressure unit cell volume of nanocrystalline e-Fe is 22.9
60.2 Å3, compared to 22.360.2 Å3 for large-grained e-Fe. No significant grain growth was
observed to occur under pressure. © 2001 American Institute of Physics.
@DOI: 10.1063/1.1357780#I. INTRODUCTION
The properties of many materials depend on crystallite
size when the size is less than 100 nm, generating a tremen-
dous amount of interest in the properties of nanocrystalline
materials and in methods for their synthesis.1 Most high-
pressure research on nanocrystalline materials has been on
semiconductors, although some work on insulators and met-
als has been reported recently. In general it has been found
that nanocrystals undergo the same phase transitions as their
large-grained counterparts, although at elevated pressures.2–4
Differences in the phase diagrams of nanocrystals and their
large-grained counterparts have been used to argue for the
possibility of synthesizing new structures using nanocrystal-
line starting materials, as has been realized recently with
nanocrystalline alumina.5 In addition, for some materials
there is evidence that the bulk modulus and equation of state
depend on crystallite size.5,6
The Young’s modulus of some nanocrystalline materials
may be a function of particle size for reasons of porosity.7
On the other hand, a Mo¨ssbauer spectrometry study on nano-
crystalline iron ~a-Fe! has indicated that the grain boundary
regions have a bulk modulus approximately 15% of that of
the interior crystalline regions.8 A simulation of nanophase
silicon has suggested that the bulk modulus of n-Si is
smaller than that of bulk Si, although the reason is not clear.9
In contrast, embedded atom method calculations predicted a
decrease in interatomic distances in nanocrystalline materials
as compared with the large-grained metals, implying an en-
hanced bulk modulus for these nanocrystals.10
Nanocrystalline iron (n-Fe) has been the subject of
many experimental and theoretical studies. Investigations on
n-Fe have reported magnetic, mechanical, thermal, and elec-
trical properties, surface passivation, and mechanical proper-
ties such as ductility, hardness, and phonon
density-of-states.11–15 Here we report the results of high
pressure x-ray diffraction experiments, performed to measure
a!Electronic mail: bcdb7@umkc.edu4790021-8979/2001/89(9)/4794/3/$18.00
Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject tothe equation of state of n-Fe. We report a bulk modulus for
the crystallites in nanocrystalline hexagonal e-Fe that differs
little from the bulk modulus of large-grained material, al-
though there seems to be a larger unit cell volume for n-Fe.
II. EXPERIMENT
Nanocrystalline iron was made by mechanical attrition
of Fe of 99.995% purity. The material was milled in a Spex
8000 mixer/mill with a hardened steel vial, lid, and balls and
a ball-to-powder weight ratio of 20:1. The vial and lid had
knife edges machined into them, which were used to make a
metal–metal seal against a copper gasket. X-ray diffraction
line shapes were analyzed with a Dk vs k extrapolation
method to determine the average crystallite size to be 10 nm.
The powders were studied before and after compaction with
a Philips EM420 transmission electron microscope operated
at 120 keV. Dark-field images showed that the crystallite
sizes were consistent with the size of 10 nm obtained from
x-ray line shapes. For comparison, a control sample was pre-
pared from some of the same powder by annealing for 0.5 h
at 700 °C in an evacuated quartz ampoule and cooled at a
rate of 50 °C/h. This resulted in a grain size larger than 50
nm, the upper limit of our methods for measurement of crys-
tallite size.
For the high-pressure x-ray diffraction ~XRD! experi-
ments, the powder samples were loaded into a Mao–Bell
type diamond cell with anvils having 350 mm culets.16 A
spring-steel gasket, with a chamber having a diameter of 160
mm, was used to contain the sample. A mixture of 4:1 metha-
nol:ethanol was also loaded into the sample compartment to
reduce the nonhydrostatic stresses. In addition, a small
amount of gold powder ~,2%! was included to determine
the pressure, using the equation of state of gold.17 X-ray
diffraction data were measured from 0 to 46 GPa under
quasihydrostatic conditions, using x-ray diffraction at beam-
line X17C of the National Synchrotron Light Source. For
comparison, x-ray diffraction patterns from the control
sample of annealed powder were measured under similar4 © 2001 American Institute of Physics
 AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
4795J. Appl. Phys., Vol. 89, No. 9, 1 May 2001 Chen et al.conditions to 55 GPa, at beamline 2–2 of the Stanford Syn-
chrotron Radiation Laboratory. The diffraction data at both
beamlines were acquired in energy dispersive mode, using
liquid nitrogen cooled Ge detectors. At X17C the detector
was positioned at 2u59.958°60.002° and at beamline 2–2
at 2u515.272°60.013°. All data were acquired at
;295 °K. An intense peak of iron oxide (Fe2O3) was also
observed in some of the diffraction patterns. The oxide is a
passivation layer confined to the surface of the powder par-
ticles.
III. RESULTS AND DISCUSSION
The transformation pressures for the a–e and e–a tran-
sitions of large-grained Fe have been well studied, using a
variety of pressure media.18 Using 4:1 methanol:ethanol as
the pressure transmitting medium for large-grained Fe, the
a–e transition begins at 14.3 GPa and is complete at 17.5
GPa, while on decompression, e-Fe starts to convert back to
a-Fe at 11.9 GPa and the transformation is complete by 7
GPa.18
The XRD patterns showed that nanocrystalline a-Fe be-
gan transforming to e-Fe when it was compressed to 10.9
FIG. 1. Representative diffraction patterns at 5.4, 10.9, 46.0, and 7.6 GPa of
quasihydrostatically compressed n-Fe. The pattern taken at 7.6 GPa is on
decompression. The peaks labeled with asterisk are ~311! of iron oxide.
FIG. 2. Interplanar d spacing of n-Fe as a function of pressure for quasihy-
drostatic compression. The closed symbols indicate data taken upon com-
pression while the open symbols represent data taken upon decompression.
The solid lines are guides.Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject toGPa. The e phase remained to 46 GPa, the highest pressure
of this study. Upon decompression, e-Fe did not transform
back to the a phase at 7.6 GPa, which was the lowest pres-
sure measured in situ. Transmission electron microscopy
showed that no e-Fe remained at 0 GPa, however. These
images also showed that the crystallite size was not changed
significantly after compaction.
The 100, 002, and 101 x-ray diffraction lines were ob-
tained at each pressure for e-Fe ~Fig. 1!. The pressure depen-
dencies of the d spacing and the unit cell volume of n-Fe
from 8 to 46 GPa are summarized in Figs. 2 and 3. We
determined the lattice parameters of n-Fe at each pressure,
using a weighted average of the d spacing, and analyzed the
data in terms of the Birch–Murnaghan ~Eulerian finite strain!
equation of state19
FV5K@121.5~42K ! f V# , ~1!
where the negative of the Eulerian strain measure f V and
normalized pressure FV are defined as
f V50.5F S VV0D
22/3
21G , ~2!
FIG. 3. Pressure dependence of the unit cell volume for n-Fe. The closed
symbols represent experimental data for quasihydrostatic compression,
while the open symbols represent data taken upon decompression. The solid
line is the best fit of the Birch–Murnaghan equation of state to the quasihy-
drostatic compression data. The dashed line is the Birch–Murnaghan equa-
tion of state of large-grained Fe ~see Ref. 22!.
FIG. 4. Pressure dependence of the unit cell volume for annealed n-Fe. All
data was taken on compression. The solid line is the best fit of the Birch–
Murnaghan equation of state to the data. The dashed line is the Birch–
Murnaghan equation of state of large-grained Fe ~see Ref. 22!. AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
4796 J. Appl. Phys., Vol. 89, No. 9, 1 May 2001 Chen et al.FV5P@3 f V~112 f V!2.5#21, ~3!
with V0 being unit cell volume at zero pressure.
For the case of e-Fe, the unit cell volume at zero pres-
sure is not directly measurable. We obtained it by extrapola-
tion using the modified Birch–Murnaghan equation of state20
G5a1bg1cg21dg31fl , ~4!
where the effective strain, g, and new normalized pressure,
G, are defined as
g50.5F S VV*D
22//3
21G , ~5!
G5P@3~112g !2.5#21, ~6!
where V* is an arbitrary reference unit cell volume. A linear
fit to Eq. ~4! yields g0 such that G(g0)50. The unit cell
volume at zero pressure, V0 , is
V05V*~112g0!21.5. ~7!
The G – g analysis gives V0 of nanocrystalline e-Fe as 22.9
60.2 Å3. The slight increase of the unit cell volume of n-Fe
over V0 of large-grained e-Fe(22.360.2 Å3) may be ac-
counted for by lattice relaxation of n-Fe.21
The intercept and slope of the P – V data, recast into the
form F – f , give the bulk modulus K and its pressure deriva-
tive K8 at zero pressure. Fits to the data yield K5179.4
68.1 GPa, and K853.5760.65 for quasihydrostatically
compressed n-Fe of the e phase. For comparison, quasihy-
drostatic XRD patterns were collected from 3.4 to 55 GPa
for our control sample of annealed powder, giving unit cell
volumes shown in Fig. 4. The G – g and F – f analysis gives
V0522.260.2 Å3, K5173.169.7 GPa, and K853.79
60.75 for our control sample. A Birch–Murnaghan fit to
data from a previous study on large-grained e-Fe yields a
bulk modulus of 16564 GPa with a K855.33(9)—this
curve is included in Figs. 3 and 4.22 Within experimental
uncertainty, the equations of state are not different for n-Fe,
our control sample of annealed n-Fe, and prior results on
large-grained e-Fe.
A previous study on the influence of temperature and
compaction pressure on the grain size of n-Fe reported grain
growth during thermal annealing, but no effect from compac-
tion pressure up to ;3 GPa.14 We used transmission electron
microscopy to check the grain size of quenched n-Fe after
compaction to 40 GPa and found no significant grain growth.
The measured x-ray line shapes also showed no significant
changes after compaction.
Our measurements were performed with modest incre-
ments in pressure, so the pressures of the a→e and the e
→a transitions were not obtained with precision. There is
some evidence that these phase transitions both occur at
lower pressures for n-Fe, but this is a subject of ongoing
study.Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject toIV. CONCLUSIONS
We performed synchrotron x-ray diffraction on nano-
crystalline e-Fe in a diamond-anvil cell to quasihydrostatic
pressures of 46 GPa. A fit of the diffraction data to the
Birch–Murnaghan equation of state yields a bulk modulus
for the crystallites of nanocrystalline e-Fe of K5179.4
68.1 GPa with K853.5760.65, similar to that of large-
grained e-Fe. However, the extrapolated initial unit cell vol-
ume of nanocrystalline e-Fe at room pressure, V0522.9
60.2 Å3, is larger than the 22.360.2 Å3 for large-grained
e-Fe, suggesting lattice relaxation in nanocrystalline materi-
als. No significant grain growth was observed to occur under
pressure.
ACKNOWLEDGMENTS
The authors thank Dr. Jingzhu Hu for help with the XRD
operation in X17C, NSLS. This work was supported by the
National Science Foundation and the Petroleum Research
Foundation.
1 A. S. Edelstein and R. C. Cammarata, Institute of Physics ~IOP, Bristol,
1996!.
2 S. H. Tolbert and A. P. Alivisatos, Science 265, 373 ~1994!.
3 S. H. Tolbert, A. B. Herhold, L. E. Brus, and A. P. Alivisatos, Phys. Rev.
Lett. 76, 4384 ~1996!.
4 C. C. Chen, A. B. Herhold, C. S. Johnson, and A. P. Alivisatos, Science
276, 398 ~1997!.
5 B. Chen, D. Penwell, L. R. Benedetti, W. Caldwell, R. Jeanloz, and M. B.
Kruger, Bull. Am. Phys. Soc. 44, 112 ~1999!.
6 S. H. Tolbert and A. P. Alivisatos, Annu. Rev. Phys. Chem. 46, 595
~1995!.
7 G. E. Fougere, L. Riester, M. Ferber, J. R. Weertman, and R. W. Siegel,
Mater. Sci. Eng., A 204, 1 ~1995!.
8 S. Trapp, C. T. Liimbach, U. Gonser, S. J. Campbell, and H. Gleiter, Phys.
Rev. Lett. 75, 3760 ~1995!.
9 J. A. Lupo and M. J. Sabochic, Nanostruct. Mater. 1, 131 ~1992!.
10 A. Kara and T. S. Rahman, Phys. Rev. Lett. 81, 1453 ~1998!.
11 C.-M. Hsu, H.-M. Lin, K.-R. Tsai, and P.-Y. Lee, J. Appl. Phys. 76, 4793
~1994!.
12 H. Y. Bai, L. L. Luo, D. Jin, and J. R. Sun, J. Appl. Phys. 79, 361 ~1996!.
13 W. Gong, H. Li, Z. Zhao, and J. Chen, J. Appl. Phys. 69, 5119 ~1991!.
14 T. R. Malow and C. C. Koch, Metall. Mater. Trans. A 29A, 2285 ~1998!.
15 B. Fultz, J. L. Robertson, T. A. Stephens, L. J. Nagel, and S. Spooner, J.
Appl. Phys. 79, 8318 ~1996!.
16 H. K. Mao, P. M. Bell, K. J. Dunn, R. M. Chrenko, and R. C. DeVries,
Rev. Sci. Instrum. 50, 1002 ~1979!.
17 D. L. Heinz and R. Jeanloz, J. Appl. Phys. 55, 885 ~1984!.
18 R. Boehler, N. Vonbargen, and A. Chopelas, J. Geophys. Res. B 95,
21731 ~1990!.
19 F. Birch, J. Geophys. Res. B 83, 1257 ~1978!.
20 R. Jeanloz, Geophys. Res. Lett. 8, 1219 ~1981!.
21 H.-K. Mao, W. A. Bassett, and T. Takahashi, J. Appl. Phys. 38, 272
~1967!.
22 H. K. Mao, Y. Wu, L. C. Chen, and J. F. Shu, J. Geophys. Res. B 95,
21737 ~1990!. AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


Nanocrystalline iron at high pressure

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Nanocrystalline iron at high pressure

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