A Mossbauer Spectrometry Study of Thermally-Activated Electronic Processes in Li_xFePO_4

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.

Adiabatic Electron-Phonon Interaction and High-Temperature Thermodynamics of the A15 Compounds V_3X

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.

Phonon Density of States of LaFeAsO_1-xF_x

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.

Electron-Phonon Interactions and High-Temperature Thermodynamics of Vanadium and its Alloys

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.

Valence Fluctuations of ^{57}Fe in Disordered Li_{0.6}FePO_4

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.

Charge Redistribution and Phonon Entropy of Vanadium Alloys

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.

Negative entropy of mixing for solutions of vanadium-platinum

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.

Vibrations of micro-eV energies in nanocrystalline microstructures

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.

Vibrational Entropy of Spinodal Decomposition in FeCr

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.

The Entropy of Li Intercalation in Li_xCoO_2

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.

Site-specific long-range order in (Fe3Al)-Fe-57 measured by Mossbauer diffractometry

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.

Phonon entropy of alloying and ordering of Cu-Au

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.

High Lithium Capacity in Nanophase Silicon

Electrochem. Solid State Letters (9): A194-A197 Sept. 2003

J. Graetz, C. C. Ahn, R. Yazami, B. Fultz
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125}

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.

Vibrational Modes in Nanocrystalline Iron Under High Pressure

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.

The Entropy and Enthalpy of Lithium Intercalation into Graphite

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.

MÖSSBAUER DIFFRACTOMETRY

NATO Advanced Research Workshop on Mossbauer Spectroscopy in Materials Science

B. FULTZ AND J.Y.Y. LIN
California Institute of Technology, Pasadena, CA 91125 USA

1. Introduction
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.

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.

Vibrational and electronic entropy of beta-cerium and gamma-cerium measured by inelastic neutron scattering

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.

Distributions of Hydrogen and Strains in LaNi_5 and LaNi_4.75Sn_0.25

J. Alloys and Compounds 335 (2002) pp. 165-175.

B. Fultz and C. K. Witham
Engineering and Applied Science, mail 138-78,
California Institute of Technology, Pasadena, California 91125

and
T. J. Udovic
NIST Center for Neutron Research
National Institute of Standards and Technology
100 Bureau Dr., MS 8562, Gaithersburg, MD 20899-8562

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.

The temperature dependence of the phonon entropy of vanadium

Phys. Rev. B B 65 (2001) 014303-1 to 6.

P. D. Bogdanoff and B. Fultz
Keck Laboratory of Engineering Materials, mail 138-78, California Institute of Technology, Pasadena, California 91125, USA

J. L. Robertson and L. Crow
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831

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.

Intensities of Mossbauer powder diffractions from bcc ^{57}Fe

Phys. Rev. B 65 (2001) 024405.

U. Kriplani, J. Y. Y. Lin, M. W. Regehr*, B. Fultz
California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena CA 91125
* Jet Propulsion Laboratory, mail 171-113, Pasadena CA 91125

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.

Large harmonic softening of the phonon density-of-states of uranium

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.

The Character of Dislocations in LiCoO_2

Electrochemical and Solid-State Letters (submitted)

H. Gabrisch, R. Yazami*, B. Fultz
Division of Engineering and Applied Science, mail 138-78
California Institute of Technology, Pasadena, California 91125, USA

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.

Grain Boundaries of Nanocrystalline Materials - their Widths, Compositions, and Internal Structures

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.

Electron energy-loss spectrometry on lithiated graphite

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.

Atom cluster and vibrational excitations in chemically-disordered (Pt3Fe)-Fe-57

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
2 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, 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.

The phonon entropy of the martensitic transformation in NiTi

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.

Methods in Materials Research: Chapter 11. Electron Methods

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.

Methods in Materials Research: Chapter 9. Nuclear and Electron Resonance Spectroscopies

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.

Hydrogen adsorption and cohesive energy of single-walled carbon nanotubes

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.

Structural Relaxation within the Grain Boundaries of Nanocrystalline Ni_3Fe

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.

A 119Sn Mössbauer Spectrometry Study of Li-SnO Anode Materials for Li-Ion Cells

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
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

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.

Vibrational Entropy of Cu_3Au Measured by Inelastic Neutron Scattering

Phys. Rev. B, in press

P. D. Bogdanoff and B. Fultz
Division of Engineering and Applied Science, mail 138-78 California Institute of Technology, Pasadena, CA 91125
and

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.

Phonon densities of states of gamma-cerium and delta-cerium measured by inelastic neutron scattering

Philos. Mag. Lett., in press.

J. L. Robertson, Oak Ridge National Laboratory P.O. Box 2008, Oak Ridge TN 37831
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

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.

Mossbauer Diffraction and Interference Studies of Polycrystalline Metals and Alloys

Hyperfine Interactions, in press.

B. Fultz and T. A. Stephens
Engineering and Applied Science, 138-78 California Institute of Technology Pasadena, California 91125, USA

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.

A Small Angle Neutron Scattering Study of Magnetic Moments at Grain Boundaries and Magnetic Domains in Nanocrystalline Ni₃Fe

J. Appl. Phys., in press

H. N. Frase and B. Fultz
Division of Engineering and Applied Science, mail 138-78 California Institute of Technology, Pasadena, CA 91125
and

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 mu_B in the grain boundary magnetic moments after the 265 C annealing, even though there was little change in the grain boundary atomic density.

HYDROGEN DESORPTION AND ADSORPTION MEASUREMENTS ON GRAPHITE NANOFIBERS

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.

Phonons in nanocrystalline Ni₃Fe

Phys. Rev. B 57, 898 (1998)

H. Frase¹, B. Fultz¹ and J. L. Robertson²
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

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.

Two-Phase Coexistence in Fe-Cu Alloys Synthesized by Ball Milling

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.

Phonons in nanocrystalline ⁵⁷Fe

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
2 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, 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.