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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The u 3 si 2 -H system

U 3 Si 2 is of interest to the nuclear industry as a candidate fuel material due to its high uranium density and high thermal conductivity. However, it has been observed to react with hydrogen, resulting in material decrepitation. As a result, it is important to understand the thermodynamics of the U 3 Si 2 -H system. In this study, the thermodynamics of the hydrogen absorption reaction of USi were determined experimentally using Sievert’s gas absorption and related to crystallographic evolution with hydrogen content using X-ray diffraction. Experimentally-determined thermodynamic parameters were compared with results from density functional theory modeling. Results from this study were also compared with those determined in previous work. Sievert’s gas absorption results were used to develop the pressure-composition-temperature (PCT) curves of the U 3 Si 2 -H system. It was found that the hydride phase exhibited a maximum stoichiometry between U 3 Si 2 H 1.8 and U 3 Si 2 H 2 . The two-phase region for hydride formation from U 3 Si 2 exhibited a miscibility gap with a critical temperature between 623 and 673 K, as calculated from the PCT curves. Analysis of the PCT curves also showed that both the enthalpy and entropy of the hydrogen absorption reaction increased with hydrogen content but were lower than the values for uranium trihydride formation from uranium metal. The enthalpy of reaction for hydrogen absorption was calculated to range between -86.9 and -94.8 kJ mol -1 , while the entropy of reaction was calculated to range between 101.9 and 138.8 J mol -1 K -1 . Furthermore, DFT modeling of the thermoydnamic stability of the USi hydride phases yielded a decomposition temperature of U 3 Si 2 H 2 of approximately 600 K, which was consistent with the experimental results. Similarly, the DFT-calculated enthalpy and entropy of reaction to form USiH were determined to be -106.5kJ mol and 121.8J mol -1 K -1 , respectively, which were both in close agreement with the experimentally-determined values.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Phonon spectrum in the spin-Peierls phase of CuGeO 3

CuGeO 3 has long been studied as a prototypical example of the spin-Peierls transition in a 𝑆 = 1/2 Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

density functional theory↗
DOE OSTI2024

Exploring Spin‐Orbit Effects in a [Cu 6 Tl] + Nanocluster Featuring an Uncommon Tl−H Interaction

Reaction of [CuH(PPh 3 )] 6 with 1 equiv. of Tl(OTf) results in formation of [Cu 6 TlH 6 (PPh 3 ) 6 ][OTf] ([1]OTf]), which can be isolated in good yields. Variable-temperature 1 H NMR spectroscopy, in combination with density functional theory (DFT) calculations, confirms the presence of a rare Tl−H orbital interaction. According to DFT, the 1 H chemical shift of the Tl-adjacent hydride ligands of [1] + includes 7.7 ppm of deshielding due to spin-orbit effects from the heavy Tl atom. In conclusion, this study provides valuable new insights into a rare class of metal hydrides, given that [1][OTf] is only the third isolable species reported to contain a Tl−H interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Efficient computational search for lanthanide-binding additive dopants for advanced U-Zr based fuels

A rational design strategy combining theory and experiment is highly desirable for the development of U-Zr based fuels that are resistant to lanthanide-induced fuel-cladding chemical interaction (FCCI). Here, we performed rapid computational screening of FCCI-mitigating (via strong lanthanide-binding) elements across the periodic table by utilizing three simple criteria and density functional theory (DFT) calculated total energies of relevant elements and compounds retrieved from high-throughput DFT databases. In addition to successfully identifying previously demonstrated additives, our search leads to the discovery of Bi as a highly effective element among all 68 elements screened, and its effectiveness was experimentally confirmed in this study.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Surface directed reversible imidazole ligation to nickel(ii) octaethylporphyrin at the solution/solid interface: a single molecule level study

Scanning tunneling microscopy (STM) is used to study for the first time the reversible binding of imidazole (Im) and nickel(II) octaethylporphyrin (NiOEP) supported on highly oriented pyrolytic graphite (HOPG) at the phenyloctane/NiOEP/HOPG interface at 25 °C. The ligation of Im to the NiOEP receptor while not observed in fluid solution is readily realized at the solution/HOPG interface. The coordination process scales with increasing Im concentration and can be effectively modeled by the Langmuir isotherm. At room temperature it is determined that the standard free energy of adsorption is ΔG c = -15.8 kJ mol -1 and the standard enthalpy of adsorption is estimated to be ΔH c ≈ -80 kJ mol -1 . The reactivity of imidazole toward NiOEP adsorbed on HOPG is attributed to charge donation from the graphite stabilizing the Im–Ni bond. This charge transfer pathway is supported by molecular and periodic modeling calculations which indicate that the Im ligand behaves as a π-acceptor. DFT calculations also show that the nickel ion in the Im–NiOEP/HOPG complex is in a singlet ground state. This is surprising since both our calculations and previous experimental studies find a triplet ground state for the five and six coordinated Im–nickel(II) porphyrins in the gas-phase or in solution. Both the experimental and the theoretical findings provide information that is useful for better understanding of chemical sensing/recognition and catalytic processes that utilize metal–organic complexes adsorbed on surfaces where the reactivity of the metal is moderated by the substrate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

Does Chirality Influence the Stability of Amino Acid –Cu Complexes in the Salt-Induced Peptide Formation Reaction? Insights from Density Functional Theory Calculations

The polymerization of amino acids into peptides and ultimately proteins is critical to evolution of life. Ribosomally-synthesized proteins are homochiral, composed entirely of L-amino acids. Abiotic syntheses of amino acids, however, produce racemic mixtures(equal amounts of L and D enantiomers), meaning that the pool of monomers available for abiotic protein synthesis would be racemic or nearly so. There are no prebiotically plausible mechanisms known to yield homochiral peptides from racemic pools of amino acids. While some mechanisms capable of producing or amplifying enantiomeric excesses have been observed, these excesses are small or not applicable to all biologically relevant amino acids. As a result, a prebiotically-feasible mechanism to create enantiopure pools of amino acids has not been identified. However, it is not clear that these enantio-enriched or enantiopure pools are necessary to produce homochiral peptides. Steric and electronic effects, or a combination of both, may influence how different enantiomers interact with each other, potentially leading to homochiral peptides from racemic mixtures. Here, we use density functional theory (DFT) calculations to assess the stability of homochiral and heterochiral reactive complexes produced during polymerization via the salt-induced peptide formation (SIPF) reaction. Experimental studies of the SIPF reaction have shown that it enables the formation of peptides under diverse environmental conditions, making it a plausible pathway to peptide formation on early Earth. In the SIPF reaction, NaCl acts as a condensation reagent while a divalent metal cation, primarily Cu2+, facilitates polymerization by complexing and activating amino acids forming a monochlorocuprate complex. To assess if hetero-or homochiral monochlorocuprate complexes were energetically favored, we compared the stability of LL, DD, and LD enantiomers of Cu2+–(alanine)2and Cu2+–(valine) 2 complexes. Gaussian 09 density DFT energy-minimization calculations were made for each Cu –amino acid complex in the cis and trans configuration. Models were energy minimized using the BH and HLYP/6-31++G(d,p) level of theory and free energies were compared to determine the most stable configuration.

A C Fox↗
DOE OSTI2025

Bonding and reactivity of isostructural uranyl and neptunyl peroxide phases

Understanding the reactivity of actinide peroxides is critical for predicting the behavior of spent nuclear fuel in radiolytic environments. Herein, we report the synthesis and characterization of a lithium neptunyl(VI) hydroxo peroxo compound (LiNp), which is isostructural to the uranyl analogue (LiU). Single-crystal X-ray diffraction reveals that LiNp contains both [NpO 2 (O 2 ) 3 ] 4- and [NpO 2 (OH) 4 ] 2- units stabilized by Li + and hydrogen bonding and Raman spectroscopy shows systematic redshifts in neptunyl vibrational modes relative to uranyl. DFT calculations highlight the importance of secondary coordination in reproducing vibrational and structural features, but challenges remain with correctly modeling strong sigma donors. Solid-state EPR spectroscopy and DFT confirm superoxide stabilization within LiU and calculations suggest favorability of the analogous radical species in LiNp. Solution state EPR spectroscopy with the radical spin trap 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide (BMPO) reveal evidence of superoxide in the LiU and LiNp phases and suggests stabilization of superoxide within actinyl triperoxide complexes, forming [AnO 2 (O 2 ) 2 (O) 2 • ] 3- .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

High-Energy Hybridized States Enable Long-Lived Hot Electrons in Cobaloxime-Silicon Nanocrystal System

Strong electronic coupling is achieved between the molecular catalyst cobaloxime ([Co]) and silicon nanocrystals (Si NCs) bridged by an ethylenepyridine group derived from vinylpyridine (vpy) covalently bound to the Si NC surface (Si-vpy-[Co]). The ethylenepyridine tether in Si-vpy-[Co] is key to dramatic changes to the system’s physical properties which are not observed in the corresponding formylpyridine (fpy) system (Si-fpy-[Co]) consistent with strong electronic coupling previously observed only in dark electrochemical systems. UV−vis absorption spectroscopy reveals new [Co]-centered electronic states in Si-vpy-[Co], and transient absorption spectroscopy finds a strong absorption feature appearing within 250 fs and persisting for at least 5 ns. Astoundingly, spectroelectrochemical measurements reveal that this absorption feature is consistent with both the singly reduced [Co] − and doubly reduced [Co] 2− complexes, leading to the conclusion that these long-lived charges are derived from high-energy “hot” electrons residing in [Co]-centered states. Detailed analysis using cyclic voltammetry, spectroelectrochemistry, electron paramagnetic resonance spectroscopy, and density functional theory (DFT) calculations provides insight into the unique electronic structure created in Si-vpy-[Co]. DFT reveals that the new electronic states arise from hybridization between deep Si NC band states and high-energy molecular orbitals of the ethylenepyridine tether and the [Co] catalyst and are facilitated by σ-bonding character at the ethylenepyridine linkage. This study demonstrates that strong electronic coupling achieved through precise molecular chemistry can change the paradigm of otherwise fixed energy levels in hybrid photoelectrochemical systems for artificial photosynthesis and related applications.

14 SOLAR ENERGY↗
DOE OSTI2014

Stress effects on the initial lithiation of crystalline silicon nanowires: Reactive molecular dynamics simulations using ReaxFF

Silicon (Si) has been recognized as a promising anode material for the next-generation high-capacity lithium (Li)-ion batteries because of its high theoretical energy density. Recent in situ transmission electron microscopy (TEM) revealed that the electrochemical lithiation of crystalline Si nanowires (c-SiNWs) proceeds by the migration of the interface between the lithiated Si (LixSi) shell and the pristine unlithiated core, accompanied by solid-state amorphization. The underlying atomic mechanisms of Li insertion into c-Si remain poorly understood. In this research, we perform molecular dynamics (MD) simulations using the reactive force field (ReaxFF) to characterize the lithiation process of c-SiNWs. Our calculations show that ReaxFF can accurately reproduce the energy barriers of Li migration from DFT calculations in both crystalline (c-Si) and amorphous Si (a-Si). The ReaxFF-based MD simulations reveal that Li insertion into interlayer spacing between two adjacent (111) planes results in the peeling-off of the (111) facets and subsequent amorphization, in agreement with experimental observations. We find that breaking of the Si–Si bonds between (111)-bilayers requires a rather high local Li concentration, which explains the atomically sharp amorphous–crystalline interface (ACI). Our stress analysis shows that lithiation induces compressive stress at the ACI layer, causing retardation or even the stagnation of the reaction front, also in good agreement with TEM observations. Lithiation at high temperatures (e.g. 1200 K) shows that Li insertion into c-SiNW results in an amorphous to crystalline phase transformation at Li : Si composition of ~4.2:1. In conclusion, our modeling results provide a comprehensive picture of the effects of reaction and diffusion-induced stress on the interfacial dynamics and mechanical degradation of SiNW anodes under chemo-mechanical lithiation.

25 ENERGY STORAGE↗
DOE OSTI2020

A Bayesian analysis of nuclear deformation properties with Skyrme energy functionals

In spite of numerous scientific and practical applications, there is still no comprehensive theoretical description of the nuclear fission process based solely on protons, neutrons and their interactions. Furthermore, the most advanced simulations of fission are currently carried out within nuclear density functional theory (DFT). In spite of being fully quantum-mechanical and rooted in the theory of nuclear forces, DFT still depends on a dozen or so parameters characterizing the energy functional. Calibrating these parameters on experimental data results in uncertainties that must be quantified for applications. This task is very challenging because of the high computational cost of DFT calculations for fission. In this paper, we use Gaussian processes to build emulators of DFT models in order to quantify and propagate statistical uncertainties of theoretical predictions for a range of nuclear deformations relevant to describing the fission process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces

The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.

Chemical processes↗
DOE OSTI2023

Conventional High-Temperature Superconductivity in Metallic, Covalently Bonded, Binary-Guest C–B Clathrates

Inspired by the synthesis of XB 3 C 3 (X = Sr, La) compounds in the bipartite sodalite clathrate structure, density functional theory (DFT) calculations are performed on members of this family containing up to two different metal atoms. A DFT chemical pressure analysis on systems with X = Mg, Ca, Sr, Ba reveals that the size of the metal cation, which can be tuned to stabilize the B–C framework, is key for their ambient-pressure dynamic stability. High-throughput density functional theory calculations on 105 Pm$\bar{3}$ symmetry XYB 6 C 6 binary-guest compounds (where X, Y are electropositive metal atoms) find 22 that are dynamically stable at 1 atm, expanding the number of potentially synthesizable phases by 19 (18 metals and 1 insulator). Here, the density of states at the Fermi level and superconducting critical temperature, T c , can be tuned by changing the average oxidation state of the metal atoms, with T c being highest for an average valence of +1.5. KPbB 6 C 6 , with an ambient-pressure Eliashberg T c of 88 K, is predicted to possess the highest T c among the studied Pm$\bar{3}$n XB 3 C 3 or Pm$\bar{3}$XYB 6 C 6 phases, and calculations suggest it may be synthesized using high-pressure high-temperature techniques and then quenched to ambient conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ru-promoted perovskites as effective redox catalysts for CO2 splitting and methane partial oxidation in a cyclic redox scheme

The current study reports AxA’1-xByB’1-yO3- perovskite redox catalysts (RCs) for CO2-splitting and methane partial oxidation (POx) in a cyclic redox scheme. Strontium (Sr) and iron (Fe) were chosen as A and B site elements with A’ being lanthanum (La), samarium (Sm) or yttrium (Y), and B’ being manganese (Mn), or titanium (Ti) to tailor their equilibrium oxygen partial pressures (P_(O_2 ) s) for CO2-splitting and methane partial oxidation. DFT calculations were performed for predictive optimization of the oxide materials whereas experimental investigation confirmed the DFT predicted redox performance. The redox kinetics of the RCs improved significantly by 1 wt.% ruthenium (Ru) impregnation without affecting their redox thermodynamics. Ru impregnated LaFe0.375Mn0.625O3 (A=0, A’=La, B=Mn, and B’=0) was the most promising RC in terms of its superior redox performance (CH4/CO2 conversion >90% and CO selectivity~ 95%) at 800oC. Long-term redox testing over Ru impregnated LaFe0.375Mn0.625O3 indicated stable performance during the first 30 cycles following with a ~25% decrease in the activity during the last 70 cycles. Air treatment was effective to reactivate the redox catalyst. Detailed characterizations revealed the underlying mechanism for redox catalyst deactivation and reactivation. Furthermore, this study not only validated a DFT guided mixed oxide design strategy for CO2 utilization but also provides potentially effective approaches to enhance redox kinetics as well as long-term redox catalyst performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

An adaptive genetic algorithm for crystal structure prediction

We present a genetic algorithm (GA) for structural search that combines the speed of structure exploration by classical potentials with the accuracy of density functional theory (DFT) calculations in an adaptive and iterative way. This strategy increases the efficiency of the DFT-based GA by several orders of magnitude. This gain allows a considerable increase in the size and complexity of systems that can be studied by first principles. The performance of the method is illustrated by successful structure identifications of complex binary and ternary intermetallic compounds with 36 and 54 atoms per cell, respectively. The discovery of a multi-TPa Mg-silicate phase with unit cell containing up to 56 atoms is also reported. Such a phase is likely to be an essential component of terrestrial exoplanetary mantles.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4a Raw Data

Calculated formation energy of (0001 ̅) c-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (0001 ̅) c-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗
DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4b Raw Data

Calculated formation energy of (1010 ̅) m-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (1010 ̅) m-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗
DOE OSTI2014

Density functional theory and evolution algorithm calculations of elastic properties of AlON

Different models for aluminum oxynitride (AlON) were calculated using density functional theory and optimized using an evolutionary algorithm. Evolutionary algorithm and density functional theory (DFT) calculations starting from several models of AlON with different Al or O vacancy locations and different positions for the N atoms relative to the vacancy were carried out. The results show that the constant anion model [McCauley et al., J. Eur. Ceram. Soc. 29(2), 223 (2009)] with a random distribution of N atoms not adjacent to the Al vacancy has the lowest energy configuration. The lowest energy structure is in a reasonable agreement with experimental X-ray diffraction spectra. The optimized structure of a 55 atom unit cell was used to construct 220 and 440 atom models for simulation cells using DFT with a Gaussian basis set. Cubic elastic constant predictions were found to approach the experimentally determined AlON single crystal elastic constants as the model size increased from 55 to 440 atoms. The pressure dependence of the elastic constants found from simulated stress-strain relations were in overall agreement with experimental measurements of polycrystalline and single crystal AlON. Calculated IR intensity and Raman spectra are compared with available experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗