A thermodynamic criterion for selection of gas compositions for diamond deposition

Isoactivity lines for carbon with respect to diamond as the standard state have been calculated in the ternary system C-H-O at 1223 K to identify the diamond deposition domain. The gas composition is calculated by suppressing the formation of all condensed forms of carbon using the SOLGASMIX free-energy minimization program. Thirty six gas species were included in the calculation. From the gas composition, isoactivity lines are computed using recent data on the Gibbs energy of diamond. Except for activities less than 0.1, the isoactivity lines are almost linear on the C-H-O ternary diagram. Gas compositions which generate activity of diamond ranging from 1 to 100 at 1223 K fall inside a narrow wedge originating from the point representing CO. This wedge is very similar to the revised lens-shaped diamond growth domain identified by Bachman et al., using inputs from experiment. The small difference between the calculated and observed domains may be attributed to variation in the supersaturation required for diamond deposition with gas composition. The diamond solubility in the gas phase along the isoactivity line for a(di)=100 and P=6.7 kPa exhibits a minimum at 1280 K, which is close to the optimum temperature found experimentally. At higher supersaturations, non-diamond forms of carbon, including amorphous varieties, are expected. The results suggest that thermodynamic calculations can be useful for locating diamond growth domains in more complex CVD systems containing halogens, for which very little experimental data is available.

The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, Xi-Xj=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.

Computation of thermodynamic properties of liquid ferrous alloys from structural measurements

Relation between X-ray scattering intensities, mean square thermal fluctuations and thermodynamic properties. High temperature X-ray diffraction study of liquid Fe-Ni and Fe-Si alloys using reflection and transmission geometries. Calculation of the structure factor as a function of wave vector. Extrapolation to zero wave vector. Calculation of the concentration-concentration correlation function defined by A. B. Bhatia and D. E. Thorton. Computation of thermodynamic quantities of mixing A G, LlH and LlS for the binary alloys. Comparison with direct thermodynamic measurements reported in the literature.

A thermodynamic interpretation of the zonal arrangement of minerals in the bedded manganese deposits of the Noda tamagawa mine, Japan

Calculated phase relations in the system MnOSi02-C02-02 were used to propose a thermodynamic explanation for the thermal metamorphism of rhodochrosite beds lying between chert strata. The metamorphic MnOS i 0 2 minerals are arranged in order quartz(chert), rhodonite. tephroite and manganosite-hausmannite-pyrochroite rhodonite across the ore bed. The calculation covered temperatures up to 1000 K and pressures up to 5 kb. The zoning was interpreted as the result of a continuous rise in metamorphic temperature. The equilibrium partner of rhodochrosite changed from rhodonite through manganosite. Across the ore bed there are gradients in the chemical potential of MnO and SiO2 but fugacities of volatlle components such as C02. 02 and H20 were probably uniform at any given time and location during formation of the zones. Assuming that the total pressure and the fugacity of C02 were at 1.4 kb and 1.0 1 b. respectively. rhodonite. tephroite and manganosite would have formed at 472. 478 and 629 K.

Calculation of Chemical Potentials and Occupancies in Clathrate Hydrates through Monte Carlo Molecular Simulations

The flexibility of the water lattice in clathrate hydrates and guest-guest interactions has been shown in previous studies to significantly affect the values of the thermodynamic properties, such as chemical potentials and free energies. Here we describe methods for computing occupancies, chemical potentials, and free energies that account for the flexibility of water lattice and guest-guest interactions in the hydrate phase. The methods are validated for a wide variety of guest molecules, such as methane, ethane, carbon dioxide, and tetrahydrodfuran by comparing the predicted occupancy values of guest molecules with those obtained from isothermal isobaric semigrand Monte Carlo simulations. The proposed methods extend the van der Waals and Platteuw theory for clathrate hydrates, and the Langmuir constant is calculated based on the structure of the empty hydrate lattice. These methods in combination with development of advanced molecular models for water and guest molecules should lead to a more thermodynamically consistent theory for clathrate hydrates.

Methods for melting temperature calculation

Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly.

We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the melting temperature is a design criterion.

We present in detail two examples of refractory materials. First, we demonstrate how key material properties that provide guidance in the design of refractory materials can be accurately determined via ab initio thermodynamic calculations in conjunction with experimental techniques based on synchrotron X-ray diffraction and thermal analysis under laser-heated aerodynamic levitation. The properties considered include melting point, heat of fusion, heat capacity, thermal expansion coefficients, thermal stability, and sublattice disordering, as illustrated in a motivating example of lanthanum zirconate (La₂Zr₂O₇). The close agreement with experiment in the known but structurally complex compound La₂Zr₂O₇ provides good indication that the computation methods described can be used within a computational screening framework to identify novel refractory materials. Second, we report an extensive investigation into the melting temperatures of the Hf-C and Hf-Ta-C systems using ab initio calculations. With melting points above 4000 K, hafnium carbide (HfC) and tantalum carbide (TaC) are among the most refractory binary compounds known to date. Their mixture, with a general formula Ta_xHf_1-xC_y, is known to have a melting point of 4215 K at the composition Ta₄HfC₅, which has long been considered as the highest melting temperature for any solid. Very few measurements of melting point in tantalum and hafnium carbides have been documented, because of the obvious experimental difficulties at extreme temperatures. The investigation lets us identify three major chemical factors that contribute to the high melting temperatures. Based on these three factors, we propose and explore a new class of materials, which, according to our ab initio calculations, may possess even higher melting temperatures than Ta-Hf-C. This example also demonstrates the feasibility of materials screening and discovery via ab initio calculations for the optimization of "higher-level" properties whose determination requires extensive sampling of atomic configuration space.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Theoretical estimation of thermodynamic properties of the system PS/PPO on the basis of modified combining rule of Sanchez-Lacombe lattice fluid model

The three scaling parameters described in Sanchez-Lacombe lattice fluid theory (SLLFT), T*, P* and rho* of pure polystyrene (PS), pure poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and their mixtures are obtained by fitting corresponding experimental pressure volume-temperature data with equation-of-state of SLLFT. A modified combining rule in SLLFT used to match the volume per mer, v* of the PS/PPO mixtures was advanced and the enthalpy of mixing and Flory-Huggins (FH) interaction parameter were calculated using the new rule. It is found that the difference between the new rule and the old one presented by Sanchez and Lacombe is quite small in the calculation of the enthalpy of mixing and FH interaction parameter and the effect of volume-combining rule on the calculation of thermodynamic properties is much smaller than that of energy-combining rule. But the relative value of interaction parameter changes much due to the new volume-based combining rule. This effect can affect the position of phase diagram very much, which is reported elsewhere [Macromolecules 34 (2001) 6291]

Determination of micelle/water partition coefficients and associated thermodynamic data for dialkyl phthalate esters

Micelle/water partition coefficients for three dialkyl phthalate esters - dimethyl phthalate ester (DMP), diethyl phthalate ester (DEP) and dipropyl phthalate ester (DPP) were obtained by micellar liquid chromatography (MLC). Experiments were conducted over a temperature range which led to calculation of a Gibbs free energy, enthalpy and entropy of transfer for the phthalate esters. In addition, small angle neutron scattering (SANS) experiments were conducted with no substantial change observed in micelle size before and after phthalate ester incorporation. Overall, a novel method for obtaining thermodynamic information, based on partitioning data, has been developed for dialkyl phthalate esters using micellar liquid chromatography.

Calculation of the magnetic field penetration depth for high-Tc cuprate superconductors based on the Interlayer Pair Tunneling model /

In this work, the magnetic field penetration depth for high-Tc cuprate superconductors is calculated using a recent Interlayer Pair Tunneling (ILPT) model proposed by Chakravarty, Sudb0, Anderson, and Strong [1] to explain high temperature superconductivity. This model involves a "hopping" of Cooper pairs between layers of the unit cell which acts to amplify the pairing mechanism within the planes themselves. Recent work has shown that this model can account reasonably well for the isotope effect and the dependence of Tc on nonmagnetic in-plane impurities [2] , as well as the Knight shift curves [3] and the presence of a magnetic peak in the neutron scattering intensity [4]. In the latter case, Yin et al. emphasize that the pair tunneling must be the dominant pairing mechanism in the high-Tc cuprates in order to capture the features found in experiments. The goal of this work is to determine whether or not the ILPT model can account for the experimental observations of the magnetic field penetration depth in YBa2Cu307_a7. Calculations are performed in the weak and strong coupling limits, and the efi"ects of both small and large strengths of interlayer pair tunneling are investigated. Furthermore, as a follow up to the penetration depth calculations, both the neutron scattering intensity and the Knight shift are calculated within the ILPT formalism. The aim is to determine if the ILPT model can yield results consistent with experiments performed for these properties. The results for all three thermodynamic properties considered are not consistent with the notion that the interlayer pair tunneling must be the dominate pairing mechanism in these high-Tc cuprate superconductors. Instead, it is found that reasonable agreement with experiments is obtained for small strengths of pair tunneling, and that large pair tunneling yields results which do not resemble those of the experiments.

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

Ab initio calculation of the BCC Fe-Al-Mo (Iron-Aluminum-Molybdenum) phase diagram: Implications for the nature of the tau(2) phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe-Al-Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order-disorder equilibrium between Fe(3)Al-D0(3) and FeAl-B2 is increased by Mo additions, while the critical temperature for the FeAl-B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2-(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the tau(2) phase, stable at high temperatures in overstoichiometric B2-FeAl. (C) 2009 Elsevier Ltd. All rights reserved.

Prediction of dopant atom distribution on nanocrystals using thermodynamic arguments

A theoretical approach aiming at the prediction of segregation of dopant atoms on nanocrystalline systems is discussed here. It considers the free energy minimization argument in order to provide the most likely dopant distribution as a function of the total doping level. For this, it requires as input (i) a fixed polyhedral geometry with defined facets, and (ii) a set of functions that describe the surface energy as a function of dopant content for different crystallographic planes. Two Sb-doped SnO2 nanocrystalline systems with different morphology and dopant content were selected as a case study, and the calculation of the dopant distributions expected for them is presented in detail. The obtained results were compared to previously reported characterization of this system by a combination of HRTEM and surface energy calculations, and both methods are shown to be equivalent. Considering its application pre-requisites, the present theoretical approach can provide a first estimation of doping atom distribution for a wide range of nanocrystalline systems. We expect that its use will support the reduction of experimental effort for the characterization of doped nanocrystals, and also provide a solution to the characterization of systems where even state-of-art analytical techniques are limited.

Renormalization-group calculation of dynamical properties for impurity models

The numerical renormalization-group method was originally developed to calculate the thermodynamical properties of impurity Hamiltonians. A recently proposed generalization capable of computing dynamical properties is discussed. As illustrative applications, essentially exact results for the impurity specttral densities of the spin-degenerate Anderson model and of a model for electronic tunneling between two centers in a metal are presented. © 1991.

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using Complete Basis Set and Gaussian-n Models combined with CPCM Continuum Solvation Methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pKa values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol, to calculate pKa values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001