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Changes in the local electronic structure at atoms around Li sites in the olivine phase of LiFePO4 were studied during delithiation. Electron energy loss spectrometry was used for measuring shifts and intensities of the near-edge structure at the K-edge of O and at the L-edges of P and Fe. Electronic structure calculations were performed on these materials with a plane-wave pseudopotential code and with an atomic multiplet code with crystal fields. It is found that both Fe and O atoms accommodate some of the charge around the Li+ ion, evidently in a hybridized Fe−O state. The O 2p levels appear to be fully occupied at the composition LiFePO_4. With delithiation, however, these states are partially emptied, suggestive of a more covalent bonding to the oxygen atom in FePO_4 as compared to LiFePO_4. The same behavior is found for the white lines at the Fe L_(2,3)-edges, which also undergo a shift in energy upon delithiation. A charge transfer of up to 0.48 electrons is found at the Fe atoms, as determined from white line intensity variations after delithiation, while the remaining charge is compensated by O atoms. No changes are evident at the P L_(2,3)-edges.

Instrumentation was developed to study the thermodynamics of lithium intercalation in cokes that were heat-treated at different temperatures. The method measures the open circuit voltages of electrochemical cells as a function of temperature, and obtains the entropy and enthalpy of the lithiation reaction. X-ray diffractometry and Raman spectroscopy were used to determine the structure of the carbon materials after heat treatment. The effect of the degree of graphitization on the entropy and enthalpy of lithium intercalation was thereby determined. A model is proposed to correlate the degree of graphitization to entropy profiles. It is shown that graphs of entropy versus open circuit voltage for different states of charge give quantitative information on graphitization, making them useful for the structural characterization of partially-graphitized carbons.

The local electronic structure around iron ions in Li0.6FePO4 was studied by 57Fe Mossbauer spectrometry at temperatures from 25 to 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 solid solution compared to the two-phase material at temperatures of 130 °C and above. Fluctuations in the electric field gradient showed an approximately Arrhenius behavior, with an activation energy of 335 ± 25meV and a prefactor of 5 × 1011 Hz, whereas Arrhenius plots for the isomer shift showed activation energies of approximately 600 meV. It is suggested that these 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. Overall, the disordered solid solution phase shows faster electronic dynamics than the...

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., Comment: 7 pages, 6 figures, supplemental material (3 figures)

Inelastic neutron scattering measurements on monoclinic zirconia (ZrO_2) and 8 mol% yttrium-stabilized zirconia were performed at temperatures from 300 to 1373wK. Temperature-dependent phonon densities of states (DOS) are reported, as are Raman spectra obtained at elevated temperatures. First-principles lattice dynamics calculations with density functional theory gave total and partial phonon DOS curves and mode Grüneisen parameters. These mode Grüneisen parameters were used to predict the experimental temperature dependence of the phonon DOS with partial success. However, substantial anharmonicity was found at elevated temperatures, especially for phonon modes dominated by the motions of oxygen atoms. Yttrium-stabilized zirconia (YSZ) was somewhat more anharmonic and had a broader phonon spectrum at low temperatures, owing in part to defects in its structure. YSZ also has a larger vibrational entropy than monoclinic zirconia.

MCViNE (Monte-Carlo VIrtual Neutron Experiment) is a versatile Monte Carlo (MC) neutron ray-tracing program that provides researchers with tools for performing computer modeling and simulations that mirror real neutron scattering experiments. By adopting modern software engineering practices such as using composite and visitor design patterns for representing and accessing neutron scatterers, and using recursive algorithms for multiple scattering, MCViNE is flexible enough to handle sophisticated neutron scattering problems including, for example, neutron detection by complex detector systems, and single and multiple scattering events in a variety of samples and sample environments. In addition, MCViNE can take advantage of simulation components in linear-chain-based MC ray tracing packages widely used in instrument design and optimization, as well as NumPy-based components that make prototypes useful and easy to develop. These developments have enabled us to carry out detailed simulations of neutron scattering experiments with non-trivial samples in time-of-flight inelastic instruments at the Spallation Neutron Source. Examples of such simulations for powder and single-crystal samples with various scattering kernels, including kernels for phonon and magnon scattering, are presented. With simulations that closely reproduce experimental results, scattering mechanisms can be turned on and off to determine how they contribute to the measured scattering intensities, improving our understanding of the underlying physics., 34 pages, 14 figures

Inelastic neutron scattering was performed on silicon powder to measure the phonon density of states (DOS) from 100 to 1500 K. The mean fractional energy shifts with temperature of the modes were $\ensuremath{\langle}\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{i}/{\ensuremath{\varepsilon}}_{i}\ensuremath{\Delta}T\ensuremath{\rangle}=\ensuremath{-}0.07$, giving a mean isobaric Gr\"uneisen parameter of $+6.95\ifmmode\pm\else\textpm\fi{}0.67$, which is significantly different from the isothermal parameter of +0.98. These large effects are beyond the predictions from quasiharmonic models using density functional theory or experimental data, demonstrating large effects from phonon anharmonicity. At 1500 K the anharmonicity contributes $0.15{k}_{\mathrm{B}}$/atom to the vibrational entropy, compared to $0.03{k}_{\mathrm{B}}$/atom from quasiharmonicity. Excellent agreement was found between the entropy from phonon DOS measurements and the reference NIST-JANAF thermodynamic entropy from calorimetric measurements.

Recent measurements of the phonon spectra of several Au-rich alloys of face-centered-cubic Fe-Au using inelastic neutron scattering and nuclear-resonant inelastic x-ray scattering are summarized. The Wills-Harrison model, accounting for charge transfer upon alloying, is used to explain the observed negative excess vibrational entropy of mixing, which increases the miscibility gap temperature in the system by an estimated maximum of 550 K and we adjudicate to a charge transfer from the Fe to the Au atoms that results in an increase in the electron density in the free-electron-like states and in stronger sd-hybridization. When Au is the solvent, this softens the Fe–Fe bonds but stiffens the Au–Au and Au–Fe bonds which results in a net stiffening relative to the elemental components.

The lithium-storage material Li(0.6)FePO(4) was studied by inelastic neutron scattering and differential scanning calorimetry. Li(0.6)FePO(4) undergoes a transformation from a two-phase mixture (heterosite and triphylite) to a disordered solid-solution at 200 degrees C. Phonon densities of states (DOS) obtained from the inelastic neutron scattering were similar for the two-phase sample measured at 180 degrees C and the disordered sample measured at 220 degrees C. The vibrational entropy of transformation is 1.8 +/-0.9 J/(K mol), which is smaller than the configurational entropy difference of approximately 3.1 J/(K mol). The measured enthalpy of the disordering transition was estimated as 2.5 kJ/mol. The phonon data show a small change in lattice dynamics upon disordering.

Cathodes based on cubic (spinel) structure LiMn2O4 were investigated by electrochemical entropymetry in an attempt to characterize their phase diagram according to the initial lithium composition. The stoichiometric material shows a very pronounced 2-phase region in the high 4V plateau and a solid- solution behavior in the lower 4V plateau. A third region is found in the non stoichiometric material characterized by a steep increase in entropy. This may relate to the onset of a stoichiometry induced anticipated cubic to tetragonal phase transition in the 4V area in this material. The later has been so far reported to occur only in the 3V area.

The phase diagram for LixFePO4 has been determined for different lithium concentrations and temperatures. X-ray diffraction analysis was used to determine phase fractions at temperatures between room temperature and 400 oC for LixFePO4 at different states of lithiation. The two low- temperature phases, heterosite and triphylite, have previously been shown to transform to a disordered solid solution at elevated temperatures. This disordered phase allows for a continuous transition between the heterosite and triphylite phases and is stable at relatively low temperatures. At intermediate temperatures the proposed phase diagram resembles a eutectoid system, with eutectoid point at around x=0.6 and 200oC. Kinetics of mixing and unmixing transformations are reported, including the hysteresis between heating and cooling. The enthalpy of this transition is at least 700 J/mol.

Inelastic neutron scattering measures the dynamical processes in materials, as opposed to spatial arrangements of atoms. A neutron diffraction pattern is obtained from measurements of the momentum transfer between the neutron and the sample. Inelastic neutron scattering includes the additional dimension of energy. This paper explains concepts, describes instrumentation, and gives a few materials applications for inelastic neutron scattering.

The low-temperature martensitic phase transformation in Fe71Ni29 was studied by X-ray diffractometry, differential scanning calorimetry (DSC) and inelastic neutron scattering. From inelastic neutron scattering spectra, the phonon density of states of the high-temperature austenite and low-temperature martensite were obtained, showing a substantial stiffening in the martensite phase. The change in vibrational entropy associated with this stiffening was found to be . Using published results for the Fe partial density of states in disordered BCC Fe–Ni of similar composition, a Ni partial density of states was obtained, which shows a significant number of modes at much lower energies than its Fe counterpart. The martensitic and reverse-martensitic transformations occur at different temperatures and the total entropies of transformation were measured by DSC for both. From these measurements and published magnetisation results for this alloy, it is found that the change in magnetic entropy is twice as large as ...

Alloying with Si is shown to destabilize the strongly bound hydrides LiH and MgH2. For the LiH/Si system, a Li2.35Si alloy forms upon dehydrogenation, causing the equilibrium hydrogen pressure at 490 °C to increase from approximately 5 × 10-5 to 1 bar. For the MgH2/Si system, Mg2Si forms upon dehydrogenation, causing the equilibrium pressure at 300 °C to increase from 1.8 to >7.5 bar. Thermodynamic calculations indicate equilibrium pressures of 1 bar at approximately 20 °C and 100 bar at approximately 150 °C. These conditions indicate that the MgH2/Si system, which has a hydrogen capacity of 5.0 wt %, could be practical for hydrogen storage at reduced temperatures. The LiH/Si system is reversible and can be cycled without degradation. Absorption/desorption isotherms, obtained at 400−500 °C, exhibited two distinct flat plateaus with little hysteresis. The plateaus correspond to formation and decomposition of various Li silicides. The MgH2/Si system was not readily reversible. Hydrogenation of Mg2Si appears...

Mössbauer powder diffractometry was used to study partially-ordered 57Fe3Al. Multiple diffraction patterns were measured at Doppler velocities across all nuclear resonances in the sample. The superlattice diffractions were analyzed to provide data on the long-range order of Fe atoms having different numbers of Al neighbors. Comparing experimental data to calculations showed that Fe atoms having three Al atoms as first-nearest neighbors (1nn) have simple cubic long-range order, similar to that of Fe atoms with four Al 1nn. The simple cubic periodicity of Fe atoms with three Al 1nn was significantly lower than expected for homogeneous antisite disorder, however. Monte-Carlo simulations and transmission electron microscopy suggest that a significant fraction of aperiodic Fe atoms with three Al 1nn are near antiphase domain boundaries.

Mossbauer powder diffractometry was used to study puerility ordered 57 Fe 3 Al. 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 (INNS) have partial sc long-range order, similar to that of Fe atoms with four Al lNNs. The Fe atoms with two Al lNNs had partial fcc order similar to that of Fe atoms with zero Al lNN. No evidence was found for B32 order for any of the Fe environments.

Changes in the electronic structure of Li_(1-x)Ni_(0.8)Co_(0.2)O_2 during delithiation (charge) are elucidated by changes in the O K-edge and transition-metal (TM) L_(2,3)-edge. Electron energy-loss spectrometry was used to investigate the O 2p and TM 3d occupancy over a wide range of lithium concentrations. Quantitative analysis of the TM L_(2,3) white lines indicates that the Ni ion accommodates no more than one-half of an electron, whereas the net Co valence is unaffected by delithiation. In contrast with the small changes observed in the TM L_(2,3)-edge, a large decrease in state occupancy is observed in the near-edge structure of the O K-edge, suggesting that much of the electron charge is accommodated by the anion.

A brief survey is given of the various classes of metal alloys and compounds that are suitable for hydrogen-storage and energy-conversion applications. Comparisons are made of relevant properties including hydrogen absorption and desorption pressures, total and reversible hydrogen-storage capacity, reaction-rate kinetics, initial activation requirements, susceptibility to contamination, and durability during long-term thermal cycling. Selected applications are hydrogen storage as a fuel, gas separation and purification, thermal switches, and sorption cryocoolers.

The electronic structure of chemically delithiated Li_(1-x)CoO_2 (x = −0.02, 0.09, 0.12, 0.20, and 0.28) was investigated by electron energy-loss spectrometry (EELS). The O K edge and Co L_(2,3) edge were used to probe the density of unoccupied states around the O and Co ions at different states of lithiation. The O ions accommodate the incoming charge during Li intercalation. The net electron density surrounding the Co ions is less affected. This is in substantial agreement with prior electronic structure calculations of Van der Ven, et al., whose atomic structure data were used in the present calculations of EELS cross-sections. Calculations of the O 2p partial densities of state curves confirm the increase in unoccupied states that accompany Li extraction.

A Mossbauer powder diffractometer was used to measure diffraction patterns from polycrystalline 57Fe3Al. The intensities of Bragg diffractions were measured when the incident γ-rays were tuned to different resonances of the Mossbauer spectrum. The bcc fundamental diffractions were strong, and superlattice diffractions of (1/2 1/2 1/2) and (1 0 0) families were measurable. The 57Fe local environments with 0 Al and 4 Al first-nearest-neighbors had the periodicities expected from their sites in the perfect D03 unit cell, but the long-range periodicity of the 3 Al environment was also measured. This disordered site had a surprisingly high degree of B2 long-range order.

Inelastic nuclear resonant scattering spectra of 57Fe atoms were measured on Pt3 57Fe and Pd3 57Fe with the L12 crystal structure, and with the same crystallographic sites for 57Fe atoms. Phonon partial density of states curves for 57Fe were obtained from these spectra. In comparison to the non-dispersive Einstein-like optical modes in Pt3 57Fe, the optical modes in Pd3 57Fe are broader. This difference can be understood in terms of the difference in mass of Pd and Pt.

Valence fluctuations of Fe^(2+) and Fe^(3+) 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 enthalpies 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 large, 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.

Part III describes the important and established families of phase transitions in materials. Chapters 10–16 describe structural and chemical phase transformations of materials that occur by movements of atoms. These include heterogeneous first-order transitions such as melting and precipitation, and spinodal decomposition and ordering that may occur homogeneously as second-order phase transitions. Martensite and other displacive phase transitions are the subject of Chapter 15, and microstructural and nanostructural aspects of phase transformations are covered in Chapter 16. All these phase transitions involving atom rearrangements are historical figures in the field of materials science, and new phenomena are often explained with reference to them. Chapter 17 describes some of the major phase transitions involving electrons and spins that occur inside materials. Electronic and magnetic phase transitions can sometimes be understood with similar approaches as phase transformations involving atom rearrangements, but some aspects of electronic or magnetic excitations are not classical. This is emphasized in Chapter 18, which ends by touching on quantum criticality. Research on quantum phenomena such as superconductivity is often reliant on controlling the structures of materials. Likewise, results from condensed matter physics offer new insights into phase transformations in materials.

This book explains the thermodynamics and kinetics of most of the important phase transitions in materials science. It is a textbook, so the emphasis is on explanations of phenomena rather than a scholarly assessment of their origins. The goal is explanations that are concise, clear, and reasonably complete. The level and detail are appropriate for upper division undergraduate students and graduate students in materials science and materials physics. The book should also be useful for researchers who are not specialists in these fields. The book is organized for approximately linear coverage in a graduate-level course. The four parts of the book serve different purposes, however, and should be approached differently.

Magnetism in materials originates with electron spins and their alignments. Groups of spins develop patterns and structures at low temperatures through interactions with each other. With temperature, pressure, and magnetic field, these spatial patterns of electron spins are altered, and several trends can be understood by thermodynamic considerations. This chapter describes how magnetic structures change with temperature. The emphasis is on magnetic moments localized to individual atoms, as may arise from unpaired 3 d electrons at an iron atom, for example. The strong intra atomic exchange interaction gives an atom a robust magnetic moment, but the magnetic moments at adjacent iron atoms interact through inter atomic exchange interactions. Interatomic exchange interactions are often weaker, having energies comparable to thermal energies. Interatomic exchange is analogous to chemical bonding between pairs of atoms in a binary alloy that develops chemical order. The critical temperature of chemical ordering T c corresponds to the Curie temperature for a magnetic transition T C , and short-range chemical order above the T c finds an analog in the Curie–Weiss law for paramagnetic susceptibility above T C . For chemical ordering the atom species are discrete types, whereas magnetic moments can vary in strength and direction as vector quantities. This extra freedom allows for diverse magnetic structures, including antiferromagnetism, ferrimagnetism, frustrated structures, and spin glasses.

The field of phase transitions is rich and vast, and continues to grow. This text covers parts of the field relevant to materials physics, but many concepts and tools of phase transitions in materials are used elsewhere in the larger field of phase transitions. Likewise, new methods from the larger field are now being applied to studies of materials. Part I of the book covers essential topics of free energy, phase diagrams, diffusion, nucleation, and a few classic phase transformations that have been part of the historical backbone of materials science. In essence, the topics in Part I are the thermodynamics of how atoms prefer to be arranged when brought together at various temperatures, and how the processes of atom movements control the rates and even the structures that are formed during phase transformations. The topics in Part I are largely traditional ones, but formulating the development in terms of statistical mechanics and in terms of the kinetic master equation allows more rigor for some topics, and makes it easier to incorporate a higher level of detail from Part II into descriptions of phase transitions in Parts III and IV.