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At least 127 records · Page 7

Ab initio modeling and thermodynamics of hydrated plutonium oxalates

An ab initio study on the plutonium oxalate hydrates: Pu 2 (C 2 O 4 ) 3 ·10H 2 O and Pu(C 2 O 4 ) 2 ·6H 2 O, using PBE exchange-correlation with D3 dispersion correction and Hubbard correction for the plutonium atoms, was performed and compared to experimental vibrational spectral and thermodynamic property values. Here we demonstrated that this technique can accurately predict the experimental infrared spectra Pu(III) oxalate hydrate, as well as the Raman peak of PuO 2 (used to calculate the thermodynamic properties of the oxalates). For Pu(IV) oxalate hydrate we found that our predicted structure agreed qualitatively with PXRD measurements, the only available experimental determination of the structure. Using this method at standard temperature and pressure, we predicted standard enthalpies of formation of -6,755 kJ mol -1 and -3,923 kJ mol -1 and standard Gibbs free energy of formation of -5,899 kJ mol -1 and -3,386 kJ mol -1 for Pu 2 (C 2 O 4 ) 3 ·10H 2 O and Pu(C 2 O 4 ) 2 ·6H 2 O, respectively.

36 MATERIALS SCIENCE↗

Thermal properties and Thermodynamic Equilibrium Modeling of Cementitious Waste Forms

INTRODUCTION Cementitious matrices are used in the US DOE complex and worldwide to solidify aqueous radioactive, hazardous, mixed salt solutions, and sludges to meet low-level radioactive waste (LLW) disposal requirements. Blended formulations are used for most waste form mix designs. Substitution of pozzolans for Class F fly ash has the potential to alter the processing properties and stabilization properties of the resulting waste forms because they add chemical and mineralogical complexity to the final material. The Savannah River Site saltstone waste form was selected as the test case material. CemGEMS software was chosen as the model for predicting hydrated cementitious phases assemblages and phase evolution. Isothermal calorimetry was used as the method for evaluating processing and properties of fresh, uncured waste forms. The test cases consisted of reference case saltstone, and five natural pozzolan substituted saltstone mixes.

Bustamante, Michael E. [Savannah River National La↗

Phase Diagrams of Alloys and Their Hydrides via On-Lattice Graph Neural Networks and Limited Training Data

Efficient prediction of sampling-intensive thermodynamic properties is needed to evaluate material performance and permit high-throughput materials modeling for a diverse array of technology applications. To alleviate the prohibitive computational expense of high-throughput configurational sampling with density functional theory (DFT), surrogate modeling strategies like cluster expansion are many orders of magnitude more efficient but can be difficult to construct in systems with high compositional complexity. We therefore employ minimal-complexity graph neural network models that accurately predict and can even extrapolate to out-of-train distribution formation energies of DFT-relaxed structures from an ideal (unrelaxed) crystallographic representation. This enables the large-scale sampling necessary for various thermodynamic property predictions that may otherwise be intractable and can be achieved with small training data sets. Two exemplars, optimizing the thermodynamic stability of low-density high-entropy alloys and modulating the plateau pressure of hydrogen in metal alloys, demonstrate the power of this approach, which can be extended to a variety of materials discovery and modeling problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In-situ thermodynamics measurements at metal oxides-solution interfaces using Flow Adsorption Microcalorimetry.

Mineral-fluid interfaces are the principal sites of geochemical processes near Earth’s surface, hosting chemical reactions that play a fundamental role in (bio)geochemical cycles and in the fate and transport of anthropogenic contaminants, and that effectively control the compositions of soil and water environments. These complex interfaces are critical for our energy and environmental future. The mineral-fluid interface has been studied in an unprecedented level of detail with both experimental and computational approaches, separately and in combination. However, conspicuously missing from studies of the mineral-fluid interface are direct measurements of the energies of ion sorption and exchange. The literature on energetics and enthalpies of exchange, adsorption, dissolution, precipitation, and surface protonation reactions, especially those directly supported by experimental data, remains scarce despite their fundamental nature. The overarching goal of this project is to complete a systematic study of the thermodynamics properties of interfacial reactions at four MO surfaces (Rutile (α-TiO2), Quartz (SiO2), boehmite (γ-AlOOH) and goethite (α-FeOOH)) through the application and construction of novel flow adsorption microcalorimetry techniques and instrumentations. These unique and specialized microcalorimeters will operate at various temperatures and solution chemical compositions allowing for in-situ measurements across metal oxides and ligands of various characteristics. The overall research goal will be accomplished by completing the following three specific objectives (O): O1) Determine the energetics of surface protonation and deprotonation, ion exchange and ligand sorption reactions; O2) Investigate the surface charge thermodynamic properties under a range of temperature and solution chemical compositions; and O3) Develop predictive trends of the interplay between MO structure, surface coverage and surface reactivity. In addition to key thermodynamics parameters, calorimetric measurements provide a wealth of mechanistic information about reactions energetics and kinetics, surface charge characteristics, and structure-reactivity or selectivity relationships, all obtained in-situ and in real-time. This report includes science highlights from various projects completed over the performance period of the project. Also listed are dissemination opportunities, people supported on the grant and the impact on available physical resources and the discipline as a whole.

58 GEOSCIENCES↗

The solubility of La hydroxide and stability of La 3+ and La hydroxyl complexes at acidic to mildly acidic pH from 25 to 250 °C

The mobility of rare earth elements (REE) in natural hydrothermal systems can be assessed using geochemical modeling, which requires reliable thermodynamic data of relevant aqueous species. In this study, we evaluate the controls of pH and temperature on La speciation and the role of hydroxyl complexes in REE transport at hydrothermal conditions. Batch-type hydrothermal solubility experiments were conducted using synthetic La hydroxide powders equilibrated in perchloric acid-based aqueous solutions at temperatures between 150 and 250 °C and starting pH of 2 to 5. The La hydroxide solubility is retrograde with temperature and displays a strong pH dependence with a decrease in La concentrations from acidic to mildly acidic pH spanning between 3 and 5 orders of magnitude (e.g. log La molality of –2.5 to –7.2 at 250 °C). Thermodynamic optimizations using GEMSFITS allow to retrieve the standard partial molal Gibbs energies for the La 3+ aqua ion and the formation constants for the La hydroxyl species (i.e., LaOH 2+ , La(OH) 2 + , La(OH) 3 0 ) between 25 and 250 °C. A comparison between the experimentally derived thermodynamic properties with the calculated values from the Helgeson-Kirkham-Flowers equation of state parameters indicates an increased divergence with temperature. Discrepancies in standard partial molal Gibbs energies range between ~ 1 – 12 kJ/mol and result in a predicted La hydroxide solubility differing by up to 3 orders of magnitude at 250 °C. Speciation calculations indicate a higher stability of La 3+ and LaOH 2+ over the other La hydroxyl species in the studied pH range of 3.4 to 6. Here, the optimized thermodynamic properties for La aqueous species have important implications for modeling the solubility of REE minerals such as monazite and the mobility of REE in hydrothermal systems.

58 GEOSCIENCES↗

Cation Disorder of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ in Super‐Earth Mantles

Understanding the mineralogy of exoplanets is essential for unraveling their interior structures, dynamics, and evolution. For large super-Earths, the post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$, one of the major mantle phases, may undergo the order-disorder transition (ODT) at high temperatures. However, the ODT phase boundary of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ has not been rigorously constrained. Additionally, fundamental thermodynamic properties of the disordered ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ remain poorly investigated. Here, we develop a unified machine learning potential (MLP) for ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ of ab initio accuracy under super-Earth mantle conditions. With the efficient MLP, we extensively calculate the free energy of post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ via the thermodynamic integration method. The results are used to constrain the ODT phase boundary. Furthermore, we report the P-V-T equation of state and Grüneisen parameters for post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ across various degrees of disorder. These thermodynamic properties are further applied to update the adiabatic thermal profiles and the mass-radius relation of super-Earths.

36 MATERIALS SCIENCE↗

Insight into the Relationship Between Viscosity and Structure of CaO-SiO{sub 2}-MgO-Al{sub 2}O{sub 3} Molten Slags

This article elucidates the quantitative relationship between viscosity and structure in a basic slag system of CaO-SiO{sub 2}-MgO-Al{sub 2}O{sub 3} and focuses on the role of Al{sub 2}O{sub 3}. Slag viscosity was measured by the rotating cylinder method, and structural information was obtained using Fourier transformation infrared, Raman and magic angular spinning nuclear magnetic resonance (MAS-NMR) techniques. The results show that, as the Al{sub 2}O{sub 3} content increased, slag viscosity increased initially and decreased afterwards, directly indicating that Al{sub 2}O{sub 3} had an amphoteric effect on slag viscosity. The Raman spectra verified that with increasing Al{sub 2}O{sub 3} content, the concentrations of Q{sup 0}(Si) and Q{sup 2}(Si) decreased first and then increased, while that of Q{sup 1}(Si) kept increasing and that of Q{sup 3}(Si) increased first and then decreased. The {sup 27}Al MAS-NMR spectra proved that the mole ratios of AlO{sub 5} and AlO{sub 6} to AlO{sub 4} kept increasing with the increase of Al{sub 2}O{sub 3} content, and, overall, Al{sub 2}O{sub 3} changed from a network former to a network modifier. The relationship between the viscosity and structure of the molten slags was further analyzed quantitatively based on the modified (NBO/T), denoted as (NBO/T)′, and we found a fine linear correlation between the logarithm of viscosity and (NBO/T)′. Moreover, the variations of thermodynamic properties of this system also indirectly supported the present experimental results.

36 MATERIALS SCIENCE↗

From electronic structure to model application of key reactions for gasoline/alcohol combustion: Hydrogen-atom abstractions by $CH_3\dot{O}$ radical

H-atom abstraction by methoxy radical ($CH_3\dot{O}$) plays an important role in capturing the kinetics of reactions between gasoline components and alcohols. This study focuses on determining the reaction rates and thermodynamic properties of methoxy radical reactions with five gasoline fuel components: n-heptane, iso-octane, 1-hexene, cyclopentane and toluene. Electronic structure calculations were per-formed for all the stationary points with M06-2X/6 -311 ++ g(d,p) method. G3 composite method with atomization method is used for determining Δ f H 0 of all the closed shell and radical species, using which the necessary thermodynamic data of all the species was determined. Coupled cluster theory QCISD(T)/cc-pVXZ (where X = D and T) and Møller-Plesset perturbation theory MP2/cc-pVXZ (where X = D, T and Q) were used to calculate single point energies. Subsequently, rate constants for all hydrogen atom ab-straction channels have been performed using conventional transition state theory with unsymmetric tunneling corrections. A systematic comparison of rates for abstraction from different sites within the same species and same site from different species is done in order to get insights into this reaction class. Here, the computed thermodynamic properties and rate constants were incorporated into a recent gasoline mechanism to investigate the impact of the calculations performed in this work. A shift in predicted NTC (negative temperature coefficient) behavior and significant reduction in model reactivity is observed upon incorporating the rates calculated herein.

33 ADVANCED PROPULSION SYSTEMS↗

Coupled Interfacial and Bulk Kinetics Govern the Timescales of Multiphase Ozonolysis Reactions

Chemical transformations in aerosols impact the lifetime of particle phase species, the fate of atmospheric pollutants, and both climate- and health-relevant aerosol properties. Timescales for multiphase reactions of ozone in atmospheric aqueous phases are governed by coupled kinetic processes between the gas phase, the particle interface, and its bulk, which respond dynamically to reactive consumption of O 3 . However, models of atmospheric aerosol reactivity often do not account for the coupled nature of multiphase processes. Herein, to examine these dynamics, we use new and prior experimental observations of aqueous droplet reaction kinetics, including three systems with a range of surface affinities and ozonolysis rate coefficients ( trans -aconitic acid (C 6 H 6 O 6 ), maleic acid (C 4 H 4 O 4 ), and sodium nitrite (NaNO 2 )). Using literature rate coefficients and thermodynamic properties, we constrain a simple two-compartment stochastic kinetic model which resolves the interface from the particle bulk and represents O 3 partitioning, diffusion, and reaction as a coupled kinetic system. Our kinetic model accurately predicts decay kinetics across all three systems, demonstrating that both the thermodynamic properties of O 3 and the coupled kinetic and diffusion processes are key to making accurate predictions. An enhanced concentration of adsorbed O 3 , compared to gas and bulk phases is rapidly maintained and remains constant even as O 3 is consumed by reaction. Multiphase systems dynamically seek to achieve equilibrium in response to reactive O 3 loss, but this is hampered at solute concentrations relevant to aqueous aerosol by the rate of O 3 arrival in the bulk by diffusion. As a result, bulk-phase O 3 becomes depleted from its Henry's law solubility. This bulk-phase O 3 depletion limits reaction timescales for relatively slow-reacting organic solutes with low interfacial affinity (i.e., trans-aconitic and maleic acids, with k rxn ≈ 10 3 -10 4 M -1 s -1 ), which is in contrast to fast-reacting solutes with higher surface affinity (i.e., nitrite, with k rxn ≈ 10 5 M -1 s -1 ) where surface reactions strongly impact the observed decay kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bond Dissociation Energies in Heavy Element Chalcogen and Halogen Small Molecules

Thermodynamic properties including bond dissociation energies, heats of formation, and gas phase acidities for the hydrides and dimers of chalcogens and halogens: H 2 Y, HX, Y 2 and X 2 for Y = Se, Te, At and X = Br, I, and At have been predicted using the Feller-Peterson-Dixon composite correlated molecular orbital theory approach. A full 4-component CCSD(T) approach was used to calculate the spin-orbit effects on thermodynamic properties, except for Se 2 where the AoC-DHF value was used due to strong multireference effects in Se 2 for the SO calculations. The calculated results show that the At 2 bond dissociation energy is quite small, 19.5 kcal/mol, with much of the low bond energy due to spin orbit effects. H 2 Po is not predicted to be stable to dehydrogenation to Po + H 2 in terms of the free energy at 298 K. In the gas phase, HAt is predicted to be a stronger acid than H 2 SO 4 . Here, the current results provide insights into potential difficulties in the actual experimental observation of such species for heavy elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development and Validation of Physics-Based Sub-Models of High-Pressure Supercritical Fuel Injection at Diesel Conditions Insert

The project sought to develop and validate accurate, physics-based, numerical submodels and implement them in computational fluid dynamics (CFD) software codes to enable accurate predictions of diesel sprays at pressures higher than the current systems. The combined experimental-computational effort has four main objectives: (1) acquire spatially and temporally resolved scalar measurements of fuel-oxidizer mixing in the near field of the fuel jet, (2) develop software modules to calculate thermo-physical properties of diesel surrogates and their mixtures with oxidizer of interest in real-gas operating regime, (3) integrate the real-fluid model into a commercial and an open-source CFD code to simulate fuel-air mixing in high-pressure diesel sprays, and (4) assess the robustness, accuracy, and uncertainty of the integrated CFD solvers in computing diesel sprays. Project accomplishments are consistent with the original goals of the project. Although we acquired spatially and temporally resolved scalar measurements, they were limited to refractive index difference and not to thermodynamic properties such as temperature and equivalence ratio. However, we successfully developed the theoretical background needed to acquire such measurements at diesel conditions and demonstrated the capability of the RSD for scalar measurements in a canonical turbulent jet flow replicating features of the diesel jet. Additional work will be needed to implement these procedures at high-pressure, high-temperature engine-like conditions of the CPFR. Mainly, we did not anticipate the need to find the liquid boundary and its statistical features or the state relationships between refractive index and thermodynamic properties, assuming the widely known Dale-Gladstone equation would suffice. Still, efforts devoted to these tasks were essential to fulfil the goals of the project and serves as the foundation on which many of the conclusions and key contributions of this project are based. Further assessment and application of the developed CFD codes is recommended to fully realize the benefits of this research.

33 ADVANCED PROPULSION SYSTEMS↗

Analysis of Intermediates and Products from the Dehydrogenation of Mg(BH 4 ) 2

The thermodynamic properties of key compounds, Mg(B 3 H 8 ) 2 , MgB 2 H 6 , MgB 10 H 10 , Mg(B 11 H 14 ) 2 , Mg 3 (B 3 H 6 ) 2 , and MgB 12 H 12 , proposed to be formed in the release of hydrogen from magnesium borohydride Mg(BH 4 ) 2 and uptake of hydrogen by MgB 2 , have been investigated using solid–state density functional theory (DFT) calculations. Further, more accurate treatment of cell–size effects to the entropies were also investigated, in order to improve the accuracy of the thermodynamic properties of complex borohydrides. We find that the zero–point energy corrections can lower the electronic energies of reaction by 20–30 kJ/(mol H 2 ) for these intermediates, while adding the thermal and entropy contributions results in the total decrease up to ~50 kJ/(mol H 2 ). Although our treatment lowers the calculated formation energy of Mg(B 3 H 8 ) 2 , it is still too high to explain the experimental observation of B 3 H 8 – . We discuss possible reasons for this disparity and propose that the formation of B 3 H 8 – and H – in a disordered amorphous phase has a large energy difference compared to the phase–separated Mg(B 3 H 8 ) 2 and MgH 2 considered in calculations. Comparison of the experimental and NMR chemical shifts calculated within a DFT approach for known species Mg(BH 4 ) 2 , Mg(B 3 H 8 ) 2 , Mg(B 11 H 14 ) 2 , MgB 10 H 10 and MgB 12 H 12 provides validation for predicting the chemical shifts of the other compounds which are yet to be confirmed experimentally. These include MgB 2 H 6 and the proposed tri–anion species Mg 3 (B 3 H 6 ) 2 that both have favorable thermodynamics for reversible hydrogen storage in Mg(BH 4 ) 2 without the formation of MgH 2 as a co–product which could phase–separate and inhibit rehydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Overcoming significant challenges in extracting off-stoichiometric thermodynamics using the compound energy formalism through complementary use of experimental and first principles data: A case study of Ba 1-x Sr x FeO 3-δ

The compound energy formalism (CEF) is a powerful framework to describe the thermodynamics of metal oxides as a function of off-stoichiometry, temperature, and composition. The thermodynamic properties are crucial materials design attributes in metal oxide-based oxygen-exchange chemical processes. Despite the richness of information an accurate CEF model provides, a method to determine a unique and accurate fit for oxygen exchange materials remains elusive. This contribution details a method for fitting the CEF model that overcomes the current fitting challenges through three innovations: 1) the combination of density functional theory calculations with experimental data decorrelates excess terms and delineates the enthalpic/entropic contributions to the Gibbs free energy; 2) a systematic determination of the important CEF model terms, removing thermodynamic predetermining human intervention; 3) a self-consistent solution of the starting oxygen offstoichiometry (δ 0 ) of thermogravimetric measurements. Thus, our method enables the reliable extraction of off-stoichiometric metal oxide thermodynamic properties and facilitates rapid materials compositional screening, and reliable process design of systems dependent on off-stoichiometric redox-active metal oxides. We apply this method to a Ba x Sr 1-x FeO 3-δ test case. We find by systematically examining the performance of the CEF model fit with and without each innovation that all three innovations are necessary for an accurate fit. We determined that reduction enthalpy is higher and more sensitive to off-stoichiometry when the Sr fraction is large (139.5 and 185.3 kJ/mol O 2 for SrFeO 3 at δ = 0 and δ = 0.5, respectively vs. nearly constant 83 kJ/mol O 2 for BaFeO 3 ). However, the reduction entropy is mostly insensitive to Sr fraction, but highly dependent on δ suggesting larger contributions in the non-configurational entropy parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic Structures and Magnetism of Zr-, Th-, and U-based Metal-Organic Frameworks (MOFs) by Density Functional Theory

Metal-organic frameworks (MOFs) have recently gained wide interest as candidate materials for nuclear waste immobilization. While the fundamental thermodynamic properties, such as the substitution energies determine the favorability of radionuclide sequestration by utilization of a MOF matrix, the studies of MOF electronic structure reveal the role of d-, and/or f-electrons on changes in physical properties of actinide-containing materials. We use density functional theory (DFT) calculations to investigate the electronic structures of Zr-, Th-, and U-MOFs, including their electronic band structures and, where appropriate, their magnetic properties. We employ various DFT methods including DFT+U, collinear spin-polarization, spin-orbit coupling, and different flavors of exchange-correlation functionals to assess the robustness to the specific exchange-correlation functional. Unlike the Zr-, and Th-MOFs, the U-MOF is found to be sensitive to electron localization and spin; hence we explore the magnetic structure of the U-MOF in further detail.

Metal-Organic Framework, MOF, Actinides, DFT↗

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

The open-source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high-pressure limit reaction rate coefficients, and pressure-dependent rate coefficient over multi-well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q-Chem, Psi4). The software outputs high-pressure limit rate coefficients and pressure-dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse-Laplace transform of high-pressure limit rate coefficients into the energy domain, energy corrections based on bond-additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG-Py software suite (https://github.com/ReactionMechanismGenerator/RMG-Py).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synthesis, characterization, and thermodynamic study of selected K-based zeolites

Potassium-rich zeolites often occur in cementitious systems, as K{sup +} is widespread in various cementitious materials, such as Portland, blended and alkali-activated cements. The knowledge of their stability and of thermodynamic models for solid solutions with Na{sup +} and Ca{sup 2+} are critical to understand long-term development and durability in such cements. Completing previous studies on Na- and Ca-based zeolites, the current work aims to determine the thermodynamic data of 14 types of K-based zeolites, which could possibly form in cementitious systems. The zeolites were synthesized hydrothermally, exchanged with K{sup +}, and characterized thoroughly with respect to framework structures, elemental compositions, water contents, and bond variations. Their thermodynamic properties were derived from the experimental solubility data, which allowed establishing predominance diagrams in the K{sub 2}O-SiO{sub 2}-Al{sub 2}O{sub 3}-H{sub 2}O system. The K-based zeolites typically showed the lowest solubility between 0 and 100 °C, with the notable exception of Ca-gismondine and two Na-based zeolites: natrolite and Na-mordenite.

36 MATERIALS SCIENCE↗