H.L. Smith, C.W. Li, A. Hoff, G. Garrett, D.S. Kim, F.C. Yang, M.S. Lucas, T. Swan-Wood, J.Y.Y. Lin, M.B. Stone, D.L. Abernathy, M. Demetriou, and B. Fultz
Nature Physics 13, 900 (2017).
Glassy materials exist in nature and play a critical role in technology, but key diffrences between the glass, liquid and crystalline phases are not well understood. Over several decades there has been controversy about the specific heat absorbed as a glass transforms to a liquid -- does this originate from vibrational entropy or configurational entropy? Here we report direct in situ measurements of the vibrational spectra of strong and fragile metallic glasses in the glass, liquid and crystalline phases. For both types of material, the measured vibrational entropies of the glass and liquid show a tiny excess over the crystal, representing less than 5% of the total excess entropy measured with step calorimetry. These results reveal that the excess entropy of metallic glasses is almost entirely configurational in origin, consistent with the early theories of Gibbs and co-workers describing the glass transition as a purely configurational transition.
F.C. Yang, J.A. Munoz, O. Hellman, L. Mauger, M. S. Lucas, S.J. Tracy, M.B. Stone, D.L. Abernathy, Yuming Xiao, and B. Fultz
Phys. Rev. Lett. 117, 076402 (2016).
Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5 phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M5 phonon mode and an adiabatic electronphonon interaction with an unusual temperature dependence.
F. Koermann, B. Grabowski, B. Dutta, T. Hickel, L. Mauger, B. Fultz and J. Neugebauer
Phys. Rev. Lett. 113, 165503 (2014).
An ab initio based framework for quantitatively assessing the phonon contribution due to magnon-phonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnon-phonon interaction is an order of magnitude larger than the phonon shift due to lattice expansion, demonstrating the strong impact of magnetic short-range order even significantly above the Curie temperature. The framework closes the previous simulation gap between the ferro- and paramagnetic limits.
Tian Lan, C. W. Li, O. Hellman, D. S. Kim, J. A. Munoz, H. Smith, D. L. Abernathy and B. Fultz
Phys. Rev. B 92, 054304 (2015).
Although the rutile structure of TiO_2 is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000 K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO_2 from 300 to 1373 K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of 3d electrons of Ti and 2p electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.
L. Mauger, M.S. Lucas, J. A. Munoz, S. J. Tracy, M. Kresch, Yuming Xiao, Paul Chow and B. Fultz
Phys. Rev. B 90, 064303 (2014).
Phonon densities of states (DOS) of bcc alpha-57Fe were measured from room temperature through the 1044 K Curie transition and the 1185 K fcc gamma-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700 K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born-von Karman model to the experimental phonon spectra using a genetic algorithm optimization. The second-nearest-neighbor fitted axial force constants weakened signicantly at elevated temperatures. An unusually large nonharmonic behavior is reported, which increases the vibrational entropy and accounts for a contribution of 35 meV/atom in the free energy at high temperatures. The nonharmonic contribution to the vibrational entropy follows the thermal trend of the magnetic entropy, and may be coupled to magnetic excitations. A small change in vibrational entropy across the alpha-gamma structural phase transformation is also reported.
S.J. Tracy, L. Mauger, H.J. Tan, J. A. Munoz, Y.M. Xiao and B. Fultz
Phys. Rev. B 90, 094303 (2014).
Valence fluctuations of Fe2+ and Fe3+ were studied in a solid solution of Li_xFePO_4 by nuclear resonant forward scattering of synchrotron x-rays while the sample was heated in a diamond-anvil pressure cell. The spectra acquired at different temperatures and pressures were analyzed for the frequencies of valence changes using the Blume-Tjon model of a system with a fluctuating Hamiltonian. These frequencies were analyzed to obtain activation energies and an activation volume for polaron hopping. There was a large suppression of hopping frequency with pressure, giving an activation volume for polaron hopping of 5.8+-0.7 A^3. This big, positive value is typical of ion diffusion, which indicates correlated motions of polarons and Li+ ions that alter the dynamics of both. Monte Carlo simulations were used to estimate the strength of the polaron-ion interaction energy.
Nicholas P. Stadie, Maxwell Murialdo, Channing C. Ahn, and Brent Fultz
J. Amer. Chem. Soc. 135, 990 (2013).
A thermodynamic study of the enthalpy of adsorption of methane on high-surface area carbonaceous materials was carried out from 238-526 K. The absolute quantity of adsorbed methane as a function of equilibrium pressure was determined by fitting isotherms to a generalized Langmuir-type equation. The adsorption of methane on zeolite-templated carbon (ZTC), an extremely high surface-area material with a periodic arrangement of narrow micropores, shows an increase in isosteric enthalpy with methane occupancy; that is, binding energies are greater as adsorption quantity increases. The heat of adsorption rises from 14 to 15 kJ mol-1 at ambient temperature, and then falls to lower values at very high loading (above a relative site occupancy of 0.6), indicating that methane-methane interactions within the adsorption layer become significant. The effect seems to be enhanced by a narrow pore-size distribution centered at 1.2 nm, corresponding to approximately the width of two monolayers of methane, and reversible methane delivery increases by up to 20% over MSC-30 at temperatures and pressures near ambient.
H.J. Tan, H.L. Smith, L. Kim, T.K. Harding, S.C. Jones, and B. Fultz
J. Electrochem. Soc. 161, A1-A5 (2014).
The cycle lives for cathodes of nanocrystalline iron trifluoride (FeF_3) were measured in rechargeable lithium batteries at different depths of discharge. When the discharge was limited to less than one Li+ ion per FeF_3, both the cycle life and energy efficiency were considerably greater than when converting FeF_3 into Fe and LiF in deep discharge. An ex situ X-ray diffractometry (XRD) study of the FeF_3 cathode during its initial discharge to LiFeF_3 showed a continuous change of the FeF_3 diffraction pattern, indicating Li+ insertion into the rhombohedral FeF_3 causing distortion of its lattice parameters. Electrochemical cycling is most reversible when this mechanism occurs in the absence of other changes in the crystal structure. of annealing, but decreased rapidly when the bcc phase formed in the material.
Chen W. Li, Xiaoli Tang, J. A. Munoz, J. B. Keith, S. J. Tracy, D. L. Abernathy, and B. Fultz
Physical Review Letters, 107, 195504 (2011).
Cubic scandium trifluoride (ScF_3) has a large negative thermal expansion over a wide range of temperature. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF_3 from 7 to 750 K. The measured phonon densities of states (DOS) show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the DOS, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO_9 structure of ScF_3, and accounts for phonon stiffening with temperature and a signicant part of the negative thermal expansion.
J. A. Munoz, M. S. Lucas, O. Delaire, M. L. Winterrose, L. Mauger, Chen W. Li, A. O. Sheets, M. B. Stone, D. L. Abernathy, Yuming Xiao, Paul Chow, and B. Fultz
Physical Review Letters 107, 115501 (2011).
Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to measure phonon spectra of FeV as a B2 ordered compound and as a bcc solid solution. The two data sets were combined to give an accurate phonon density of states, and the phonon partial densities of states for V and Fe atoms. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2 ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy by 0.22 +- 0.03 k_B/atom, which stabilizes the ordered phase to higher temperatures. First-principles calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.
H. Smith, B. Hornbuckle, L. Mauger, B. Fu, S. Tracy, G. Thompson, M.S. Lucas, Y. Xiao, M. Hu, J. Zhao, E. Alp, and B. Fultz
Acta Materialia 61, 7466 (2013).
A nanocrystalline face-centered cubic (fcc) solid solution of 6% Fe in Cu was prepared by high-energy ball milling, and annealed at temperatures from 200 to 360 C to induce chemical unmixing. The chemical state of the material was characterized by three-dimensional atom probe microscopy, Mossbauer spectrometry and X-ray powder diffractometry. The unmixing was heterogeneous, with iron atoms forming iron-rich zones that thicken with further annealing. The phonon partial density of states (pDOS) of 57Fe was measured by nuclear resonant inelastic X-ray scattering, showing the pDOS of the as-prepared material to be that of an fcc crystal. The features of this pDOS became broader in the early stages of unmixing, but only small changes in average phonon frequencies occurred until the body-centered cubic (bcc) phase began to form. The vibrational entropy calculated from the pDOS underwent little change during the early stage of annealing, but decreased rapidly when the bcc phase formed in the material.
Hongjin Tan and Brent Fultz
J. Physical Chemistry C 115, 7787 (2011).
Two-phase mixtures of Li_0.5FePO_4 with crystal sizes as small as 25 nm were prepared by solid-state reaction, ball milling, and chemical delithiation. Mossbauer spectra of nanocrystalline Li_0.5FePO_4 found evidence for a thin layer of Fe3+ at the crystal surfaces. Spectra acquired at temperatures from 25 to 225 C showed thermally-driven electronic relaxations, where the electric field gradients (EFG) of the main Fe3+ and Fe2+ spectral components decreased with temperature. The isomer shifts (IS) of Fe3+ and Fe2+ showed similar thermal trends, indicative of valence fluctuations caused by small polaron hopping. The activation energies obtained from the temperature dependence of the EFG were 410 meV for Fe3+ and 330 meV for Fe2+, and an activation energy of 400 meV was obtained for the IS of both. The rapid valence electron hopping between Fe sites is intrinsic to electronic conductivity in Li_xFePO_4, which is calculated to be higher than most reports for bulk material.
Phys. Rev. B, 82, 184301 (2010).
Xiaoli Tang, Chen W. Li, B. Fultz
Thermal phonon broadening in aluminum was studied by theoretical and experimental methods. Using second-order perturbation theory, phonon linewidths from the third-order anharmonicity were calculated from first-principles density-functional theory (DFT) with the supercell finite-displacement method. The importance of all three-phonon processes were assessed and individual phonon broadenings are presented. The good agreement between calculations and prior measurements of phonon linewidths at 300 K and new measurements of the phonon density of states to 750 K indicates that the third-order phonon-phonon interactions calculated from DFT can account for the lifetime broadenings of phonons in aluminum to at least 80% of its melting temperature.
Press Release of June, 2009 (Also, try google: Invar pressure alchemy)
Phys. Rev. Lett. 102, 237202 (2009).
M. L. Winterrose, M. S. Lucas, A. F. Yue, I. Halevy, L. Mauger, J. A. Munoz, Jingzhu Hu, M. Lerche, and B. Fultz
Synchrotron x-ray diffraction (XRD) measurements, nuclear forward scattering (NFS) measurements,
and density functional theory (DFT) calculations were performed on L12-ordered Pd_3Fe. Measurements
were performed at 300 K at pressures up to 33 GPa, and at 7 GPa at temperatures up to 650 K. The NFS
revealed a collapse of the 57Fe magnetic moment between 8.9 and 12.3 GPa at 300 K, coinciding with a
transition in bulk modulus found by XRD. Heating the sample under a pressure of 7 GPa showed
negligible thermal expansion from 300 to 523 K, demonstrating Invar behavior. Zero-temperature DFT
calculations identified a ferromagnetic ground state and showed several antiferromagnetic states had
comparable energies at pressures above 20 GPa.
J. Phys. Chem. C 113, 2526 (2009).
H. Tan, J. Dodd, and B. Fultz
The solid solution phase of LixFePO4 with different Li concentrations,
x, was investigated by Mossbauer spectrometry at temperatures between
25 C and 210 C. The Mossbauer spectra show a temperature dependence
of their isomer shifts (EIS) and electric quadrupole splittings (EQ), typical
of thermally-activated, electronic relaxation processes involving 57Fe ions.
The activation energies for the fluctuations of EQ and EIS for Fe3+ are
large nearly the same (570±9 meV), and suggest that these originate with
the charge hopping processes in LixFePO4. For the Fe2+ components of
the spectra, the fluctuations of EQ occurred at lower temperatures than
the fluctuations of EIS, with an activation energy of (512±12 meV meV)
for EQ and (551±7 meV) for EIS. The more facile fluctuations of EQ for
Fe2+ are evidence for local motions of neighboring Li+ ions. It appears
that the electron hopping frequency is lower than that of ions. The activation
energies of relaxation did not have a measurable dependence on
the concentration of lithium, x.
Phys. Rev. Lett. 101, 105504 (2008)
O. Delaire, M.S. Lucas, M. Kresch, and B. Fultz
Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds
V_3Si, V_3Ge, and V_3Co at temperatures from 10 to 1273 K. It was found that phonons in V_3Si and V_3Ge,
which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing
temperature, whereas phonons in V3Co have a normal softening behavior. First-principles calculations
show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic
electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of
sharp peaks in the electronic density of states of V_3Si and V_3Ge, which tends to decrease the electronic
density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence
the phonon thermodynamics at temperatures exceeding 1000 K.
Phys. Rev. Lett., 101, 157004 (2008). (Also Published online in: Virtual Journal of Applications of Superconductivity (October 15, 2008) Vol. 15 (8) http://www.vjsuper.org/super/ )
A.D. Christianson, M.D. Lumsden, O. Delaire, M.B. Stone, D.L. Abernathy, M.A. McGuire, A.S. Sefat, R. Jin, B.C. Sales, D. Mandrus, E.D. Mun, P.C. Canfield, J.Y.Y. Lin, M. Lucas, M. Kresch, J.B. Keith, B. Fultz, E.A. Goremychkin, and R.J. McQueeney
We have studied the phonon density of states (PDOS) in LaFeAsO1-xFx with inelastic neutron scattering
methods. The PDOS of the parent compound is very similar to the PDOS of samples optimally
doped with fluorine to achieve the maximum Tc. Good agreement is found between the experimental
PDOS and first-principles calculations with the exception of a small difference in Fe mode frequencies.
The PDOS reported here is not consistent with conventional electron-phonon mediated superconductivity.
Phys. Rev. B, 77, 214112 (2008)
O. Delaire, M.G. Kresch, J. Munoz, M.S. Lucas, J.Y.Y. Lin, and B. Fultz,
Inelastic neutron scattering was used to measure the phonon densities of states (DOSs) for pure V and solid
solutions of V with 6 to 7at% of Co, Nb, and Pt, at temperatures from 10 K to 1323 K. Ancillary measurements
of heat capacity and thermal expansion are reported on V and V-7at%Co and used to help identify the different
sources of entropy. Pure V exhibits an anomalous anharmonic stiffening of phonons with increasing temperature.
This anharmonicity is suppressed by Co and Pt, but not by isoelectronic Nb solutes. The changes in
phonon frequency with alloying and with temperature both correlate to the decrease in electronic DOSs at the Fermi level as calculated using density functional theory. The effects of both temperature
and alloying can be understood in terms of an adiabatic electron-phonon interaction (EPI), which broadens
sharp features in the electron DOS. These results show that the adiabatic EPI can influence the phonon
thermodynamics at temperatures exceeding 1000 K, and that thermal trends of phonons may help assess the
strength of the EPI.
J. Phys. Chem. B, 110 (45): 22732-22735 Nov. 16 2006.
J. L. Dodd, I. Halevy. and B. Fultz
California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena CA 91125
The local electronic structure around iron ions in Li_{0.6}FePO_4 was studied by
^{57}Fe Mossbauer
spectrometry at temperatures from 25-240 C.
The equilibrium two-phase, triphylite plus heterosite, material
was compared to a disordered solid solution
that was obtained by quenching from a high temperature.
Substantial electronic relaxations were found in the disordered sample compared to the
two-phase sample at temperatures of 130 C and above.
Fluctuations in the electric field gradient showed an approximately Arrhenius behavior,
with an activation energy of 335 meV, and a prefactor of
5 x 10^{11} Hz.
It is suggested that the spectral relaxations are caused
by the motions of Li+ ions.
A slight relaxation at 180 C in 10% of the two-phase
material can be attributed to defects in the heterosite and triphylite phases.
Phys. Rev. Lett., 97, 245701 (2006).
O. Delaire and B. Fultz
California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena CA 91125
Effects of alloying on the lattice dynamics of vanadium were investigated using inelastic neutron
scattering. Phonon densities-of-states (DOS) were obtained for bcc solid solutions of V with 3d,
4d, and 5d transition metal solutes, from which vibrational entropies of alloying were obtained. A
good correlation is found between the vibrational entropy of alloying and the electronegativity of the
transition metal solutes. This trend is successful both across the 3d row and down columns of the
periodic table. First-principles calculations on supercells matching the experimental compositions
predicted a systematic charge redistribution in the nearest-neighbor shell around the solute atoms,
also following the Pauling and Watson electronegativity scales. The systematic stiffening of the phonons is
interpreted in terms of the modified screening properties of the electron density around the solutes.
Phys. Rev. Lett., 93 (18): Art. No. 185704 Oct. 29, 2004.
O. Delaire, T. Swan-Wood, B. Fultz
California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena CA 91125
The phonon densities of states for pure vanadium and
the solid solutions
V-6.25% Ni, V-6.25% Pd, and
V-6.25% Pt were
determined from
inelastic neutron scattering measurements.
These solutes caused large stiffenings of the phonons
compared to the phonons of the elemental constituents.
The vibrational entropies of mixing 6.25% substitutional solutes
into vanadium were, for Ni, Pd and Pt solutes,
-0.082, -0.185 and -0.272 k_B/atom, respectively.
For V-6.25% Pt, the negative vibrational entropy of mixing exceeds
the conventional positive chemical entropy of mixing.
This negative total entropy of mixing should extend to lower
concentrations of Pt, and the effect on the BCC solvus line
of the V-Pt phase diagram is discussed.
The experimental data were inverted to obtain
inter-atomic force constants by using a
Born--von Karman model with an iterative
optimization algorithm.
The stiffening of bonds responsible for the decrease of entropy was
mainly in first-nearest-neighbor solute-host bonds, and correlates in part
with the solute metallic radius.
Phys. Rev. Lett., 93 (20): Art. No. 205501 Nov. 12, 2004.
A. F. Yue, A. B. Papandrew, O. Delaire and B. Fultz
Division of Engineering and Applied Science,
California Institute of Technology, Pasadena, CA 91125
Z. Chowdhuri, R. M. Dimeo, and D. A. Neumann
NIST Center for Neutron Research, National Institute of
Standards and Technology, Gaithersburg, MD 20899
The phonon density-of-states (DOS) of nanocrystalline
bcc Fe and nanocrystalline fcc Ni_3Fe were measured by inelastic
neutron scattering in two different ranges of energy.
As has been
reported previously, the
nanocrystalline materials showed enhancements in their
phonon DOS at energies from 2 to 15 milli-eV,
compared to control samples composed of large crystals. The present
measurements were extended to energies in the micro-eV range, and
showed significant, but smaller, enhancements in the number of modes in the
energy range from 5 to 18 micro-eV.
These modes of micro-eV energies provide a long-wavelength limit
that bounds the fraction of
modes at milli-eV energies
originating with the cooperative dynamics of the nanocrystalline microstructure.
Phys. Rev. B, submitted.
T. Swan-Wood, O. Delaire and B. Fultz
California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena CA 91125
Inelastic neutron scattering spectra were measured on stoichiometric
Fe_0.5Cr_0.5 prepared as a body-centered cubic (bcc) solid solution, and
after increasing amounts of chemical un-mixing on the bcc lattice
induced by annealing the solid solution at 773 K.
These spectra were reduced by a conventional procedure
to a neutron-weighted vibrational density of states.
Mossbauer spectrometry was used to characterize the extent of decomposition
after annealing.
A neutron-weight correction was performed,
using results from the M\"{o}ssbauer spectra and
recent data on inelastic nuclear resonant scattering from
^57Fe-Cr.
The vibrational entropy of decomposition was found to
be -0.17+-0.01 kB/atom, nearly equal to the change in configurational
entropy after spinodal decomposition.
Effects of vibrational entropy on the thermodynamics of un-mixing are analyzed,
showing a large effect on the free energy with the formation of Cr-rich zones, and
a large effect on the critical temperature for spinodal decomposition
for equiatomic Fe_0.5Cr_0.5.
Phys. Rev. B, 70 (17): Art. No. 174304 Nov. 2004.
Yvan Reynier, Jason Graetz, Tabitha Swan-Wood,
Peter Rez,
Rachid Yazami and Brent Fultz
California Institute of Technology, W. M. Keck Laboratory,
Pasadena CA 91125 USA
CNRS (UMR5631)-BP75 38402 St. Martin d'Heres, France
Department of Physics and Astronomy,
Arizona State University, Tempe, AZ 85287
The entropy of lithiation of Li_xCoO_2 for
0.5 < x <= 1.0 was determined
from measurements of the temperature-dependence
of equilibrated voltages of electrochemical cells.
Changes in the entropy of the lithiation reaction were
as large as 9.0 k_B/atom, and as large as 4.2 k_B/atom
within the layered hexagonal structure of Li_xCoO_2.
Three contributions to the entropy of lithiation
for the layered hexagonal phase were assessed by
experiment and calculation.
The phonon entropy of lithiation was determined
from measurements of inelastic neutron scattering, but its
changes with lithium concentration were found to be small.
Electronic structure calculations
in the local density approximation showed that
the electronic entropy of lithiation makes
a minor contribution.
The configurational entropy from lithium-vacancy disorder
was large enough to account for most of the entropy of lithiation
if stoichiometric phases exist at the
lithium concentrations of x=1/2 and x=5/6.
The electrochemical measurements and electronic structure
calculations showed that the composition range of the two-phase
region between insulating and metallic Li_xCoO_2 is
from x=0.83 to 0.93.
J.Y.Y. Lin and B. Fultz
Philosophical Magazine 83 (22): 2621-2640 AUG 1 2003
Mossbauer powder diffractometry was used to study partially ordered (Fe3Al)-Fe-57. The intensities of fundamental and superlattice Bragg diffractions were measured at 89 Doppler velocities through all nuclear resonances in the sample. The measurements were analysed to provide data on the long-range order of Fe atoms having different numbers of Al neighbours. Energy spectra of the Bragg diffractions of Mossbauer radiations were calculated with both kinematic theory and dynamic theory. Comparing experimental data with calculations showed that Fe atoms having three and five Al atoms as first-nearest neighbours (1NNs) have partial sc long-range order, similar to that of Fe atoms with four Al 1NNs. The Fe atoms with two Al 1NNs had partial fcc order similar to that of Fe atoms with zero Al INN. No evidence was found for B32 order for any of the Fe environments.
Phys. Rev. B 68 (1): art. no. 014301 July 1 2003 P. D. Bogdanoff, T. Swan-Wood, and B. Fultz Inelastic neutron scattering spectra were measured with a time-of-flight
spectrometer on six disordered Cu-Au alloys at 300 K.
The neutron-weighted phonon DOS was obtained from a conventional
analysis of these spectra.
Several methods were developed to account for this
neutron weighting and obtain the
phonon entropy of the disordered alloys.
The phonon entropies of formation of disordered
fcc Cu-Au alloys obtained in this way were generally mutually consistent,
and were also consistent with predictions from a cluster approximation obtained
from ab-initio calculations by Ozolins,
Wolverton and Zunger.
We estimate a phonon entropy of disordering of 0.15 +- 0.05 k_B/atom in Cu_3Au
at 300 K.
A resonance mode associated with the motions of the heavy Au atoms
in the Cu-rich alloys was observed at 9 meV.
An analysis of the resonance mode provided a check on the partial
phonon entropy of Au atoms.
Electrochem. Solid State Letters (9): A194-A197 Sept. 2003
J. Graetz, C. C. Ahn, R. Yazami, B. Fultz
Nanostructured silicon clusters were prepared by gas-phase ballistic consolidation. Silicon thin films were prepared by evaporation and physical
vapor deposition. Evaporated amorphous silicon electrodes prepared on rough Ni substrates showed stable capacities of 2000 mAh/g over 50 cycles.
Ballistically-deposited silicon crystallites with a 12 nm mean diameter were prepared as electrodes on copper and nickel current collectors. These
materials showed reversible gravimetric capacities of up to 2500 mAh/g with some capacity retention after 30 cycles. Elemental analysis of a
fully-lithiated nanocrystalline electrode confirmed the insertion of 4.4 lithium atoms per silicon after the first discharge. The effect of the
electrode surface area was studied by comparing silicon ballistically-deposited onto a flat substrate to depositions on a high surface area fibrous
substrate. A prolonged cycle life (50% capacity retention after 50 cycles) was observed in the low surface area material, but these electrodes
also exhibited reduced capacities of around 1100 mAh/g. The capacity losses in the ballistically-deposited electrodes are ascribed to aggregate
decrepitation and decohesion resulting from changes in the sample volume by up to 300% during cycling. The enhanced capacity and cycle life of
nanophase silicon over bulk silicon is attributed to the high surface area and short diffusion lengths of the active material and the absence of
defects in nanostructured materials.
Phys. Rev. B, in press
Alexander B. Papandrew, Alan F. Yue, Brent Fultz, Itzhak Halevy, Wolfgang Sturhahn, Thomas S. Toellner, E. Ercan Alp and Ho-kwang Mao
California Institute of Technology, Pasadena, California
91125
Physics Department, Nuclear Research
Center-Negev, 84190 Beer-Sheva, Israel
Advanced Photon Source, Argonne National
Laboratory, Argonne, Illinois 60439
Geophysical Laboratory, Carnegie Institute of
Washington, 5251 Broad Branch Road N.W., Washington, D.C. 20015
The phonon density of states (DOS) of nanocrystalline 57Fe was
measured using nuclear resonant inelastic x-ray scattering (NRIXS) at
pressures up to 28 GPa in a diamond anvil cell. The nanocrystalline
material exhibited an enhancement in its DOS at low energies by
a factor of 2.2. This enhancement
persisted throughout the entire pressure range, although
it was reduced to about 1.7 after decompression. The low-energy
regions of the spectra were fitted to the function
A^n, giving values of n close to 2 for both the bulk
control sample and the
nanostructured sample, indicative of nearly three-dimensional
vibrational dynamics. At higher energies, the Van Hove singularities
observed in both samples were coincident in energy and remained so at
all pressures, indicating that the forces conjugate to the normal
coordinates of the nanocrystalline materials are similar to the
interatomic potentials of bulk crystals.
Y. Reynier, R. Yazami and B. Fultz
J. Power Sources 19: 850-855 Sp. Iss. SI June 1 2003
The thermodynamics of the intercalation of lithium into graphite was studied in half-cells of graphite against lithium metal. Composition-voltage curves were obtained from slow-scan electrochemical cycling. At various compositions, open circuit voltages (OCV) were measured when the cell was equilibrated at different temperatures, T. From the slope and magnitude of the OCV vs. T, the entropy and enthalpy of the lithium intercalation reaction were obtained at several lithium concentrations. The entropy comprises a configurational component at low lithium concentrations, but the negative value of the entropy of intercalation at lithium concentrations greater than x=0.2 in Li_xC_6 is best explained by a vibrational contribution. The enthalpy of intercalation is negative, but is less negative for stage-1 compound formation, indicative of some repulsion of Li atoms in LiC_6 compared to LiC_12.
NATO Advanced Research Workshop on Mossbauer Spectroscopy in Materials Science
B. FULTZ AND J.Y.Y. LIN
1. Introduction
Here we explain the basic concepts of Mossbauer diffractometry in the language of kinematical diffraction. The quantized nature of the nuclear polarizations, and their interferences with x-ray diffraction are inherently different from x-ray diffractometry. More significantly, the spectroscopic capabilities of the Mossbauer effect provide unique but powerful capabilities of Mossbauer diffractometry, not available to x-ray, electron or neutron diffractometries. We describe a Mossbauer diffractometer for measurements on ^57Fe-enriched polycrystalline samples (called a "powder" diffractometer). Some characteristic data are presented, and potential applications are discussed.
Phys. Rev. B 65 (14): art. no. 144111 APR 1 2002
M. E. Manley, R. J. McQueeney, B. Fultz, R. Osborn, G. H. Kwei, P. D. Bogdanoff Time-of-flight (TOF) inelastic neutron-scattering spectra were measured on beta-cerium (double hcp) and gamma-cerium (fcc) near the phase-transition temperature. Phonon densities of states (DOS) and crystal-field levels were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from beta- to gamma-cerium, accounting for an increase in vibrational entropy of DeltaS(vib)(gamma-beta)=(0.09+/-0.05)k(B)/atom. The entropy calculated from the crystal-field levels and a fit to calorimetry data from the literature were significantly larger in beta-cerium than in gamma-cerium below room temperature, but the difference was found to be negligible at the experimental phase-transition temperature. A contribution to the specific heat from Kondo spin fluctuations was consistent with the quasielastic magnetic scattering, but the difference between phases was negligible. To be consistent with the latent heat of the beta-gamma transition, the increase in vibrational entropy at the phase transition may be accompanied by a decrease in electronic entropy not associated with the crystal-field splitting or spin fluctuations. At least three sources of entropy need to be considered for the beta-gamma transition in cerium.
J. Alloys and Compounds 335 (2002) pp. 165-175.
B. Fultz and C. K. Witham
and
Hydrogen distributions and internal strains that accompany hydriding of
binary LaNi_5 were compared to those of the ternary alloy LaNi_4.75Sn_0.25,
which is known to have cycle life superior to that of LaNi_5 in electrochemical
cells and in gas storage applications.
X-ray diffractometry shows that the unit cell volume of the
hydride phase changes more continuously with hydrogen concentration in
LaNi_4.75Sn_0.25 than in binary LaNi_5.
Gas-phase isotherms show that the Sn atoms make significant changes
to the local chemical potential of hydrogen atoms.
Using generic hydrogen-solute interactions in Monte Carlo simulations
and physical arguments, it is shown that normal coarsening of hydride
zones will be altered, or even arrested, by hydrogen-solute interactions.
Small-angle neutron scattering shows that the distribution of deuterium in
partially-deuterated LaNi_4.75Sn_0.25 is more homogeneous than in
partially-deuterated LaNi_5, at least on the spatial scales around 100 A.
It is suggested that the more homogeneous deuterium distribution in LaNi_4.75Sn_0.25
suppresses the strain gradients that cause decrepitation of the metal hydride.
Phys. Rev. B B 65 (2001) 014303-1 to 6.
P. D. Bogdanoff and B. Fultz
J. L. Robertson and L. Crow
The phonon density-of-states (DOS) of elemental vanadium was measured by
inelastic neutron scattering at
elevated temperatures.
The effect of thermal expansion significantly
overestimates the small measured shifts in phonon energies, showing that phonon
anharmonicities are
largely cancelled by effects from
phonon-phonon scattering.
Prior meaurements of the heat capacity
and calculations of the electronic entropy of vanadium are
assessed, and the analysis
requires an explicit temperature-dependence of the phonon DOS.
Using
data from the literature, similar results are obtained
for chromium, niobium, titanium and zirconium.
Phys. Rev. B 65 (2001) 024405.
U. Kriplani, J. Y. Y. Lin, M. W. Regehr*, B. Fultz
Diffraction patterns were measured on a bcc ^{57}Fe foil using a
Mossbauer powder diffractometer with high sensitivity.
Measurements with and without a magnetic field
normal to the scattering plane
showed large differences in the diffracted intensities
of the different nuclear resonances.
These magnetic effects on diffraction intensities were interpreted successfully
with a single scattering theory developed to handle isotropic and
anisotropic
orientation distributions of hyperfine magnetic fields.
When there is coherent
interference between nuclear scattering and x-ray Rayleigh scattering,
an asymmetry in the coherent intensity of the three pairs of
diffractions for the ^{57}Fe magnetic
sextet (1,6), (2,5), (3,4) is predicted.
This is largest in the presence of a uniaxial magnetic field,
and the calculated and measured asymmetries were in good agreement.
A reduced
diffraction intensity for lines (2,5) and (3,4) caused by spin-flip incoherence
was also measured.
Effects of dynamical diffraction, if present, are shown to be small.
Phys. Rev. Lett. 86 (2001) 3076-3079.
M. E. Manley, B. Fultz, R. J. McQueeney, C. Brown, W. L. Hults, J. L. Smith,
D. J. Thoma, R. Osborn, J. L. Robertson
Time-of-flight inelastic neutron scattering spectra were measured on the three
crystalline phases of uranium at temperatures from 50 K to 1213 K.
Phonon density-of-states curves were obtained from these spectra.
For the a-phase, a large decrease in phonon energies with increasing
temperature was observed over the entire temperature range.
Analysis of the vibrational power spectrum showed that the phonon
softening originates with continuous softening of a harmonic solid,
as opposed to vibrations in anharmonic potentials.
It follows that thermal excitations of electronic states are altering
the force constants. This contradicts the assumption that temperature
effects on the electronic structure can be neglected when compared to volume effects.
Vibrational entropies of the a-b and b-g phase transitions were
(Sb-Sa)_vib = (0.15±0.1) k_B/atom and (Sg-Sb)_vib= (0.36±0.1) k_B/atom.
The former accounts for about 35% and the latter 65% of the
total entropy of the phase transition. The remaining entropy must be electronic.
Electrochemical and Solid-State Letters (submitted)
H. Gabrisch, R. Yazami*, B. Fultz
Dislocations in LiCoO_2 were observed by transmission electron microscopy (TEM),
and their Burgers vectors were determined by analysis of diffraction
contrast in tilting experiments.
The configuration of all dislocations indicates that they are glissile,
and dislocation configurations were found that are indicative of active slip planes.
Perfect dislocations of a/3<11-20> type Burgers vectors were observed on {0001} habit planes.
These perfect dislocations sometimes dissociate into Shockley partial
dislocations with a/3<10-10> type Burgers vectors.
It is noted that glide of these partial dislocations can account for
the sequence of crystal structures O3, H1-3, O1 that occur with the
delithiation of LiCoO_2.
The presence of glissile dislocations also suggests possible
damage mechanisms during cycling.
Hyperfine Interactions, in press
B. Fultz and H. N. Frase
Nanocrystalline materials contain many atoms at and near grain boundaries.
Sufficient numbers of Mšssbauer probe atoms can be situated in grain boundary
environments to make a clear contribution to the measured Mšssbauer spectrum.
Three types of measurements on nanocrystalline materials are reported here, all
using Mšssbauer spectrometry in conjunction with x-ray diffractometry,
transmission electron microscopy, or small angle neutron scattering.
By measuring the fraction of atoms contributing to the grain boundary
component in a Mšssbauer spectrum, and by knowing the grain size of the material,
it is possible to deduce the average width of grain boundaries in metallic alloys.
It is found that these widths are approximately 0.5 nm for fcc alloys and slightly
larger than 1.0 nm for bcc alloys.
Chemical segregation to grain boundaries can be measured by Mšssbauer spectrometry,
especially in conjunction with small angle neutron scattering.
Such measurements on
Fe-Cu and Fe_3Si-Nb were used to study how nanocrystalline materials could be
stabilized against grain growth by the segregation of Cu and Nb to grain boundaries.
The segregation of Cu to grain boundaries did not stabilize the Fe-Cu alloys against
grain growth, since the grain boundaries were found to widen and accept more Cu atoms
during annealing. The Nb additions to Fe3Si did suppress grain growth, perhaps because
of the low mobility of Nb atoms, but also perhaps because Nb atoms altered the chemical
ordering in the alloy.
The internal structure of grain boundaries in nanocrystalline materials prepared by
high energy ball milling is found to be unstable against internal relaxations at low
temperatures. The Mšssbauer spectra of the nanocrystalline samples showed changes in
the hyperfine fields attributable to movements of grain boundary atoms.
In conjunction with SANS measurements, the changes in grain boundary structure
induced by cryogenic exposure and annealing at low temperature were found to be
somewhat different. Both were consistent with a sharper density gradient between
the crystalline region and the grain boundary region.
Appl. Phys. Lett. 77: (2) 238-240 (2000).
Hightower A, Ahn CC, Fultz B, Rez P
Transmission electron energy-loss spectrometry was used to investigate
the electronic states of metallic Li and LiC6, which is the Li-intercalated
graphite used
in Li-ion batteries.
The Li K edges of metallic Li and LiC6 were nearly identical,
and the C K edges were only weakly affected by the presence of Li.
These
results suggest only a small charge transfer from Li to C in LiC6,
contrary to prior results from surface spectra obtained by x-ray photoelectron spectroscopy.
Effects of radiation damage and sample oxidation in the transmission
electron microscopy are also reported.
Phys. Rev. B 61: (21) 14517-14522 (2000).
B. Fultz1, T. A. Stephens1, E. E. Alp2,
M. Hu2, J. Sutter2, T. S. Toellner2 and
W. Sturhahn2
1 Div. Engineering and Applied Science, 138-78
California Institute of Technology
Pasadena, California 91125, USA
Inelastic nuclear resonant scattering spectra of Fe-57 atoms were measured on crystalline alloys
of Pt,Fe-57 that were chemically disordered, partially
ordered, and L1(2) ordered. Phonon partial density of states curves for
Fe-57 were obtained from these spectra. Upon disordering, about 10% of the spectral
intensity underwent a distinct shift from 25 to 19 meV.
This change in optical modes accounted for most of the change of the vibrational entropy of
disordering contributed by Fe atoms, which was (+0.10 +/- 0.03) k(B) (Fe atom)(-1).
Prospects for parametrizing the vibrational entropy with low-order
cluster variables were assessed. To calculate the difference in vibrational entropy
of the disordered and ordered alloys, the clusters must be large enough to
account for the abundances of several of the atom configurations of the
first-nearest-neighbor shell about the Fe-57 atoms.
Philos. Mag., in press
P. D. Bogdanoff and B. Fultz
Neutron inelastic scattering, thermal expansion measurements and
low temperature calorimetry, were used to study the entropy of
the martensite to austenite transformation in NiTi, which is 0.5±0.05 k_B/atom.
The inelastic scattering spectra were corrected for the
differing scattering amplitudes of Ni and Ti with the help of a
Born - von Karman lattice dynamics simulation.
The phonon density of states (DOS) curves so obtained account
for all the transformation entropy measured by calorimetry.
From simulations and the measured DOS,
the vibrational entropy of austenite was found to be
larger than that of martensite because the TA1 and LA
acoustic modes of austenite are softer than those of martensite.
Simulations suggest that this originates with in the first
nearest-neighbor transverse force constant.
This may also be related to the soft modes involved in the
mechanism of the martensitic transformation.
Brent Fultz, ed. in E. Kaufmann, ed., J. Wiley, just published.
Introduction (first paragraph)
This chapter describes how electrons are used to probe the microstructures of materials.
These methods are arguably the most powerful and flexible set of tools available for
materials characterization. For the characterization of structures internal to materials,
electron beam methods provide capabilities for determining crystal structure, crystal
shapes and orientations, defects within the crystals, and the distribution of atoms
within these individual crystals. For characterizing surfaces, electron methods can
determine structure and chemistry at the level of the atomic monolayer.
Brent Fultz, ed. in E. Kaufmann, ed., J. Wiley, just published.
Introduction (first paragraph)
This chapter shows how nuclear and electron resonance spectroscopies
can help solve problems in materials science.
The concept of a probe, located centrally within a material,
is common to all resonance spectroscopy techniques.
For example, the nucleus serves as the probe in nuclear magnetic
resonance (NMR), nuclear quadrupole resonance (NQR) and Mšssbauer
spectrometry. Sometimes the interest is in measuring the total numbers
of probes within a material, or the concentration profiles of probe
nuclei as in the case for basic NMR imaging. More typically,
details of the measured energy spectra are of interest.
The spectra provide the energies of photons that are absorbed by the probe,
and these are affected by the electronic configuration at the location of the probe.
It is often a challenge to relate this local electronic information to
larger features of the structure of materials.
Appl. Phys. Lett., 74: (16) 2307-2309 (1999).
Y. Ye, C. C. Ahn, C. Witham and B. Fultz
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125.
J. Liu, A. G. Rinzler, D. Colbert, K. Smith, and R. E.
Smalley
Center for Nanoscale Science and Technology, Rice Quantum Institute,
Departments of Chemistry and Physics, Rice University, Houston, TX
Hydrogen adsorption on crystalline ropes of carbon single walled nanotubes
(SWNT) was found to exceed 8 wt.%, which is the highest capacity of any carbon
material. Hydrogen is first adsorbed on the outer surfaces of the crystalline ropes.
At pressures higher than about 40 bar at 80 K, however, a phase transition occurs where
there is a separation of the individual SWNT's, and hydrogen is physisorbed on their
exposed surfaces. The pressure of this phase transition provides a tube-tube cohesive energy
for much of the material of 5 meV/C atom. The cohesive energy is influenced
strongly by the quality of crystalline order in the ropes.
Philos. Mag. B 80: (8) 1545-1554 (2000).
H. N. Frase, B. Fultz,
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena CA 91125
J. L. Robertson and S. Spooner
Oak Ridge National Laboratory
P.O. Box 2008, Oak Ridge TN 37831
Results are reported from small angle neutron scattering, SANS, and
Mössbauer spectrometry measurements on four Ni_3Fe materials;
nanocrystalline material prepared by mechanical attrition,
nanocrystalline material after an exposure to 4 K, nanocrystalline
material after temperature treatments of 100 C for 10 days, and a
control sample composed of large crystals. The thermal treatments of
the nanocrystalline materials caused changes in the intensity and the
slope of both the nuclear and magnetic scattering profiles of the SANS
measurements. The Mössbauer spectra of the nanocrystalline samples
showed changes in the hyperfine fields associated with grain boundary atoms.
The changes induced by cryogenic exposure and annealing at 100 C were
somewhat different, but both were consistent with a reduction in the
number of atoms in highly disordered regions, and a sharper density
gradient between the crystalline region and the grain boundary region.
Some grain boundary atoms in mechanically-attrited Ni_3Fe are in
energetically unfavorable positions, and move into new positions during
low temperature treatments. Atom relaxations involve a reduction in the
number of atoms in highly disordered regions, and a sharper density
gradient between the crystalline region and the grain boundary region.
J. Electrochem. Soc., 147: (1) p. 1-8 (2000)
A. Hightower, P. Delcroix, G. Le Caër, C-K. Huang,
B. V. Ratnakumar, C. C. Ahn and B. Fultz
Anode materials of SnO were charged reversibly with Li to capacities
greater than 600 mAh/g. The materials were characterized by 119Sn
Mössbauer spectro-metry at 11 K and 300 K, and by x-ray diffractometry
at 300 K. Trends in the valence of Sn were as expected when the Sn
oxides are reduced in the presence of Li. At low Li capacities the
SnO is reduced to small particles of b-Sn, and with increasing Li
capacity an alloy of Li22Sn5 is formed in the material. Although the
Li22Sn5 develops over a range of Li concentrations in the anode material,
the Li22Sn5 that forms at low Li insertions is not typical of bulk Li22Sn5
either structurally or electrochemically. The recoil-free fraction of the
Sn oxide was suppressed substantially in the anode materials, indicating a
defective oxide structure in the anode material. We monitored the changes
in the Li-SnO and Li-Sn materials during atmospheric exposure over times
up to 2 months. This oxidation process of Sn was very much the reverse
of the Sn reduction during the Li insertion, although it occurred over
a much longer time scale. We also report the temperature dependencies
of recoil-free fractions in beta-Sn, SnO2, and the alloy Li22Sn5.
Phys. Rev. B, in press
P. D. Bogdanoff and B. Fultz
S. Rosenkranz
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439
The phonon density of states of
elemental Au, Cu and Cu_3Au with L1_2 chemical order were measured by
inelastic neutron scattering and used to calculate the vibrational entropy of
formation of the ordered compound from the elemental metals. A vibrational
entropy of formation of 0.06 at 300 K was obtained, with
the vibrational entropy of the ordered alloy being larger than that of the
elemental metals. The phonon DOS of the disordered Cu_3Au was simulated by
adding the phonon DOS curves of fcc Cu, alloy, and fcc Au to match the numbers
of first nearest neighbor pairs in a disordered alloy. The vibrational entropy
obtained with this simulated DOS disagrees with calorimetric data and
theoretical estimates, indicating that the phonon DOS of disordered Cu_3Au
depends on chemical order at spatial lengths larger than is set by first nearest neighbor pairs.
Philos. Mag. Lett., in press.
J. L. Robertson,
Oak Ridge National Laboratory
P.O. Box 2008, Oak Ridge TN 37831
Inelastic neutron scattering measurements were performed on
Ce metal at temperatures near the fcc (gamma) to bcc (delta) transition,
and approximate phonon DOS curves were obtained.
A large difference in the phonon DOS of the gamma-Ce and delta-Ce was
found, providing a change in vibrational entropy at the
gamma-delta transition temperature of (0.51+-0.05) kB/atom.
To be consistent with the latent heat of the gamma-delta transition,
this large change in vibrational entropy may be accompanied
by a thermodynamically-significant change in electronic
entropy of the opposite sign.
Hyperfine Interactions, in press.
B. Fultz and T. A. Stephens
After a review of previous work on Mossbauer diffraction and
interference phenomena, the principles of the kinematical
theory of Mossbauer diffraction are presented.
The emphasis is on how the spectroscopic capabilities of the
Mossbauer effect can be used to advantage in diffraction studies
on materials and condensed matter. Experimental results from
Mossbauer powder diffractometry experiments are presented.
These results identify the difficulties of Mossbauer powder
diffraction experiments, but also demonstrate that a unique
chemical environment selectivity is possible for Mossbauer
diffraction. Future experiments in Mössbauer powder diffraction
require the development of efficient detectors, and some
possibilities are suggested.
J. Appl. Phys., in press
H. N. Frase and B. Fultz
S. Spooner and J. L. Robertson
Solid State Division, Oak Ridge National Laboratory,
Oak Ridge, TN 37831
Results are reported from Mössbauer spectrometry and small
angle neutron scattering experiments on nanocrystalline Ni3Fe.
The nanocrystalline materials were prepared by mechanical attrition
and studied in the as-milled state, after annealing at 265 C to
relieve internal stress, and after annealing 600 C to prepare
a control sample comprising large crystals. The SANS measurements
were performed for a range of applied magnetic fields.
Small differences were found in how the different samples
reached magnetic saturation.
From the SANS data obtained at magnetic saturation, we found
little difference in the nuclear scattering of the as-milled
material and the material annealed at 265 C. Reductions in
nuclear scattering and magnetic scattering were observed for the
control sample, and this was interpreted as grain growth.
The material annealed at 265 C also showed a reduction in
magnetic SANS compared to the as-milled material.
This was interpreted as an increase in magnetic moments of
atoms at the grain boundaries after a low temperature annealing.
Both Mossbauer spectroscopy and small angle neutron scattering s
howed an increase of about 0.2 muB in the grain boundary
magnetic moments after the 265 C annealing, even though there
was little change in the grain boundary atomic density.
Appl. Phys. Lett. 73, 3378 (1998).
C. C. Ahn, Y. Ye, B. V. Ratnakumar*, C. Witham, R. C. Bowman, Jr.* and B. Fultz
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125.
Graphite nanofibers were synthesized and their hydrogen desorption and
adsorption properties are reported for 77 and 300 K.
Catalysts were made by several different methods including chemical routes,
mechanical alloying and gas condensation. The nanofibers were grown by
passing ethylene and H2 gases over the catalysts at 600° C.
Hydrogen desorption and adsorption were measured using a volumetric
analysis Sieverts” apparatus, and the graphite nanofibers were
characterized by transmission electron microscopy (TEM)
Brunauer-Emmett-Teller (BET) surface area analysis.
The absolute level of hydrogen desorption measured from these
materials was typically less than 0.01 H/C atom, comparable to
other forms of carbon.
Phys. Rev. B 57, 898 (1998)
H. Frase1, B. Fultz1 and J. L. Robertson2
Inelastic neutron scattering spectra were measured to obtain the
phonon density of states (DOS) of nanocrystalline fcc Ni3Fe.
The materials were prepared by mechanical alloying, and were also
subjected to heat treatments to alter their crystallite sizes and
internal strains. In comparison to material with large crystallites,
the nanocrystalline material shows two distinct differences in its
phonon DOS. The nanocrystalline DOS was more than twice as large
at energies below 15 meV. This increase was approximately
proportional to the density of grain boundaries in the material.
Second, features in the nanocrystalline DOS are broadened substantially.
This broadening did not depend in a simple way on the crystallite
size of the sample, suggesting that it has a different physical
origin than the enhancement in phonon DOS at energies below 15 meV.
A damped harmonic oscillator model for the phonons provides a
quality factor, Qu, as low as 7 for phonons in the nanocrystalline
material. The difference in vibrational entropy of the bulk and
nanocrystalline Ni3Fe was small, owing to competing changes in the
nanocrystalline phonon DOS at low and high energies.
Acta Materialia 46, 2937 (1998).
L. B. Hong and B. Fultz,
Division of Engineering and Applied Science
California Institute of Technology, 138-78, Pasadena, California 91125
Mechanical alloying with a Spex 8000 mixer/mill operated at two
intensities was used to synthesize a series of Fe100-xCux alloys with
Cu concentrations from x = 0 to x = 49.
X-ray diffractometry was used to measure the volume fractions of the
bcc and fcc phases in the alloys. Mössbauer spectrometry was used
to determine Cu concentrations in the bcc phase, and identify
inhomogeneities in Cu concentration in the bcc phase.
With higher milling intensity, there was a narrowing of the
range of compositions for fcc plus bcc coexistence, and a shift
towards Fe-rich compositions. The composition range of two-phase
coexistence is understood in terms of heterogeneities in both
defect density and concentration.
Physical Review Letters 79, 937 (1997).
B. Fultz1, C. C. Ahn1, E. E. Alp2, W. Sturhahn2, T. S. Toellner2
1 Div. Engineering and Applied Science, 138Ð78
California Institute of Technology
Pasadena, California 91125, USA
We measured the phonon density of states (DOS) of nanocrystalline
Fe by resonant inelastic nuclear gamma-ray scattering.
The nanophase material shows large distortions of its
phonon DOS. We attribute the high energy part of it to
lifetime broadening. A damped harmonic oscillator model for
the phonons provides a low quality factor, Qu, averaging
about 5, but the longitudinal modes may have been broadened most.
The nanocrystalline Fe also shows an enhancement
in its phonon DOS at energies below 15 meV.
The difference in vibrational entropy of the bulk and
nanocrystalline Fe was small, owing to competing changes
in the nanocrystalline phonon DOS at low and high energies.
A Mossbauer Spectrometry Study of Thermally-Activated Electronic Processes in Li_xFePO_4
Adiabatic Electron-Phonon Interaction and High-Temperature Thermodynamics of the A15 Compounds V_3X
Phonon Density of States of LaFeAsO_1-xF_x
Electron-Phonon Interactions and High-Temperature Thermodynamics of Vanadium and its Alloys
Valence Fluctuations of ^{57}Fe in Disordered Li_{0.6}FePO_4
Charge Redistribution and Phonon Entropy of Vanadium Alloys
Negative entropy of mixing for solutions of vanadium-platinum
Vibrations of micro-eV energies in nanocrystalline microstructures
Vibrational Entropy of Spinodal Decomposition in FeCr
The Entropy of Li Intercalation in Li_xCoO_2
Site-specific long-range order in (Fe3Al)-Fe-57 measured by Mossbauer diffractometry
Phonon entropy of alloying and ordering of Cu-Au
California Institute of Technology, W. M. Keck Laboratory,
mail 138-78,
Pasadena CA 91125
High Lithium Capacity in Nanophase Silicon
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125}
Vibrational Modes in Nanocrystalline Iron Under High Pressure
The Entropy and Enthalpy of Lithium Intercalation into Graphite
MÖSSBAUER DIFFRACTOMETRY
Concepts, Instrumentation and Measurements
California Institute of Technology, Pasadena, CA 91125 USA
The usual incoherent scattering of Mossbauer spectrometry is not useful for Mossbauer diffractometry. The basis for Mossbauer diffractometry is the interference of coherent waves, as with the other three methods for diffraction studies on materials (x-ray, electron, and neutron). Mossbauer diffractometry uses coherent nuclear resonant scattering of gamma-ray photons. Bragg diffraction peaks then occur by the constructive interference of gamma-ray wavelets scattered by a periodic crystal of nuclei. Mössbauer diffraction was first observed in studies on single crystals, in which a remarkable "nuclear speed-up" effect [2-5] enhances the diffracted intensity at the Bragg angles. It is difficult to use these "dynamical diffraction patterns" to obtain information about the crystal structure. Our work has focused on "kinematical," or single-scattering diffraction, because of its potential for structural studies on materials at the atomic scale.
Vibrational and electronic entropy of beta-cerium and gamma-cerium measured by inelastic neutron scattering
Distributions of Hydrogen and Strains
in LaNi_5 and LaNi_4.75Sn_0.25
Engineering and Applied Science, mail 138-78,
California Institute of Technology, Pasadena, California 91125
T. J. Udovic
NIST Center for Neutron Research
National Institute of Standards and Technology
100 Bureau Dr., MS 8562, Gaithersburg, MD 20899-8562
The temperature dependence of the phonon entropy of vanadium
Keck Laboratory of Engineering Materials, mail 138-78, California
Institute of Technology, Pasadena, California 91125, USA
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge,
Tennessee 37831
Intensities of Mossbauer powder diffractions from bcc ^{57}Fe
California Institute of Technology, W. M. Keck Laboratory, mail 138-78,
Pasadena CA 91125
* Jet Propulsion Laboratory, mail 171-113,
Pasadena CA 91125
Large harmonic softening of the phonon density-of-states of uranium
The Character of Dislocations in LiCoO_2
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena, California 91125, USA
Grain Boundaries of Nanocrystalline Materials -
their Widths, Compositions, and Internal Structures
Electron energy-loss spectrometry on lithiated graphite
Atom cluster and vibrational excitations in chemically-disordered (Pt3Fe)-Fe-57
2 Advanced Photon Source, Argonne National Laboratory,
Argonne, Illinois 60439, USA
The phonon entropy of the martensitic transformation in NiTi
Methods in Materials Research: Chapter 11. Electron Methods
Methods in Materials Research: Chapter 9. Nuclear and Electron Resonance Spectroscopies
Hydrogen adsorption and cohesive energy of single-walled carbon
nanotubes
Structural Relaxation within the Grain Boundaries of Nanocrystalline Ni_3Fe
A 119Sn Mössbauer Spectrometry Study of Li-SnO Anode Materials for Li-Ion Cells
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology
Pasadena, CA 91125, USA
Laboratoire de Science et Génie des Matériaux Métalliques,
C.N.R.S. U.M.R. 7584, Ecole des Mines,
F-54042 Nancy Cedex, France
Electrochemical Technologies Group, Bldg. 277
Jet Propulsion Laboratory
Pasadena, CA 91109, USA
Vibrational Entropy of Cu_3Au Measured
by Inelastic Neutron Scattering
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena, CA 91125
and
Phonon densities of states of gamma-cerium and delta-cerium
measured by inelastic neutron scattering
H. N. Frase, B. Fultz,
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena CA 91125
R. McQueeney
Los Alamos National Laboratory, MSH805
Manuel Lujan Jr. Neutron Scattering Center
Los Alamos, NM 87545
Mossbauer Diffraction and Interference Studies of
Polycrystalline Metals and Alloys
Engineering and Applied Science, 138-78
California Institute of Technology
Pasadena, California 91125, USA
A Small Angle Neutron Scattering Study of
Magnetic Moments at Grain Boundaries and Magnetic Domains in
Nanocrystalline Ni3Fe
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena, CA 91125
and
HYDROGEN DESORPTION AND ADSORPTION MEASUREMENTS ON
GRAPHITE NANOFIBERS
Phonons in nanocrystalline Ni3Fe
1 Div. Engineering and Applied Science, 138-78
California Institute of Technology, Pasadena, California 91125, USA
2 Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge TN 37831
Two-Phase Coexistence in Fe-Cu Alloys Synthesized by Ball Milling
Phonons in nanocrystalline 57Fe
2 Advanced Photon Source, Argonne National Laboratory,
Argonne, Illinois 60439, USA