Ammonia Synthesis on Proton-enriched Palladium Substrate

Production of Ammonia is one of the most important in the chemical industry; most of the Ammonia produced is then converted to other Nitrogen-containing molecules, such as anhydrous ammonium nitrate or urea, which are typically used for inhorganic fertilizers. The standard industrial reaction for the production of Ammonia is the Haber-Bosch Process (sec. 1.1); an high-pressure and high-temperature process known and developed since the early twentieth century [31, 11]. The Haber-Bosch process produces Ammonia directly from its components, Nitrogen and Hydrogen, supplied in gas form. Although successful, this industrial process, consumes a large amount of energy which, given the huge production volume, employs a significant percentage of total world energy production and natural gas consuption [70]. Because of its economical importance, improving the Ammonia production process is still an open challenge and a rich field of research. A search in related journal archives for papers regarding Ammonia production typically returns hundreds or thousands of results; nevertheless there is still room for improvement and better understanding of the reaction. A part of the studies have been focused on improving the Haber-Bosch process itself; e.g. replacing the original Iron catalyst with more efficient metal alloys. However other studies have tried to find novel reaction mechanisms, that could possible overcome the high-pressure and high-temperature requirements. Some studies have been based on certain biological process, occuring in bacteria, that can produce Ammonia at room temperature and pressure [77, 68, 24]. In the biological process the energy required by the reaction is not supplied thermally but by reduction of adenosine triphosphate (ATP) molecules, which makes them dicult to reproduce in vitro. Another possible approach is to supply the required energy electrochemically, by applying an external electric eld to a solid-state catalyst, or having a certain amount of current circulating through it, it is possible to transfer to the reactants the necessary amount of energy. The electrical source can also act in an indirect way, modifying the nano-scale properties of the catalyst in a way that improves its properties; this eect is called non- Faradayc Electrochemical Modification of Catalytic Reaction (NEMCA) [56, 80]. In 1998 Stoukides and coworkers [50, 49] (sec. 1.2)demonstrated the possibility of producing Ammonia at atmospheric pressure by supplying the required amount of Hydrogen via a proton-conducting perovskite. The perovskite, in the form of a little brick or a pipe, is coated on two sides with a Palladium paste, obtaining two catalytic surfaces separated by a proton conductor. The two catalysts are then connected through an electrical circuit and a certain bias is applied, making them act as an anode and a cathode. When the anode is exposed to molecular Hydrogen, H2 dissociates spontaneously. Because of the bias, the Hydrogen atoms are stripped of their electron and forced to cross the proton conductor; the electron will instead travel through the external electrical circuit; recombination of protons and hydrogens happens in the cathode. The cathode itself is exposed to Nitrogen gas. Combining this electrochemical mechanism with high temperature (between 500 C and 750 C) the author were able to induce a steady ux of Ammonia, with a high conversion efficiency. They also proposed the presence of a NEMCA effect, although weak. In the present work we will re-examine the original experiment and tackle its characteristic and inner mechanics at the nano-scale level. We will use ab-initio methods (chap. 2) to construct a model of the catalytic process and simulate its intermediate steps. In our study we have used the computational tools provided by the Quantum-espresso distribution [28]. In particular we will use Density Functional Theory (sec. 2.2) and the Projector-Augmented Wave method (PAW, sec. 2.3) to reproduce the electronic structure of the system; the Born-Oppenheimer approximation, together with the Hellmann-Feynman theorem, will be implicitly used to optimize the nanoscopic structure, and find intermediate steps of the reactions. We will also used the Transition State Theory (sec. 3.3) and the Nudged- Elastic Band method (sec. 3.4) to estimate the energy barriers involved in the reaction and, consequently, the reaction rate. In chapter 4 we will examine the catalyst structure in detail; in particular we will focus on the effect of active Hydrogen pumping by mean of the applied cell potential. In section 4.1 we will see how a cell potential of realistic amplitude can force a very large amount of Hydrogen in the Palladium bulk. The resulting system, called Palladium hydride, can undergo a phase transition that changes its unit-cell volume up to 10%; we will see the details of this phase change and the possibly resulting structures. In section 4.2 we will move our focus to the catalyst surface. We will tackle the problem of determining the adsorbed Hydrogen population, in the case of normal Palaldium and Palladium hydride. This complex problem involves a three-phase equilibrium, where the chemical potentials of Hydrogen in the gas and Hydrogen adsorbed in the bulk or on the surface have to be equal. In order to estimate the chemical potential we will use a Monte Carlo simulation built on top of a simplified model where the total energy is computed as a sum of adsorption on-site energies and neighbour-site interactions. Finally, in chapter 5, we will tackle the core of the problem, trying to find a suitable reaction path for the Ammonia production. We will examine the possibility of Nitrogen dissociative adsorption as well as the possiblity of Nitrogen hydrogenation prior to its dissociation. The former will be easily proved impossible, at the experimental conditions, so we will focus on the subsequent hydrogenations of the N2 molecules. We will examine the process up to the final breaking of the N{N bond, where the formation of Ammonia can proceed without further barriers. An order of magnitude estimate of the Ammonia production in the system will be made and found to be compatible with the experimental findings

Anharmonic properties from a generalized third order ab~initio approach: theory and applications to graphite and graphene

We have implemented a generic method, based on the 2n+1 theorem within density functional perturbation theory, to calculate the anharmonic scattering coefficients among three phonons with arbitrary wavevectors. The method is used to study the phonon broadening in graphite and graphene mono- and bi-layer. The broadening of the high-energy optical branches is highly nonuniform and presents a series of sudden steps and spikes. At finite temperature, the two linearly dispersive acoustic branches TA and LA of graphene have nonzero broadening for small wavevectors. The broadening in graphite and bi-layer graphene is, overall, very similar to the graphene one, the most remarkable feature being the broadening of the quasi acoustical ZO' branch. Finally, we study the intrinsic anharmonic contribution to the thermal conductivity of the three systems, within the single mode relaxation time approximation. We find the conductance to be in good agreement with experimental data for the out-of-plane direction but to underestimate it by a factor 2 in-plane

Ab initio variational approach for evaluating lattice thermal conductivity

We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us with an algorithm faster than the one previously used in literature and able to always converge to the exact solution. Three-phonon normal and umklapp collision, isotope scattering and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than the commonly observed in isotopically enriched diamond samples with 99.93% C12 and 0.07 C13

Second order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: theory and stochastic implementation

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe

Anharmonic phonon spectra of PbTe and SnTe in the self-consistent harmonic approximation

At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depends on the approximation used for the exchange-correlation kernel in density functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the free energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe, we reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\Gamma$X direction. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high temperature Fm$\overline{3}$m structure to the low temperature R3m one.Comment: 12 pages, 15 Picture

First-principles calculations of phonon frequencies, lifetimes and spectral functions from weak to strong anharmonicity: the example of palladium hydrides

The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "$2n+1$" theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron scattering spectra in solids where the harmonic approximation breaks down and a non-perturbative approach is required to deal with anharmonicity. To validate our approach, we calculate the anharmonic phonon linewidth in the strongly anharmonic palladium hydrides. We show that due to the large anharmonicity of hydrogen optical modes the inelastic neutron scattering spectra are not characterized by a Lorentzian line-shape, but by a complex structure including satellite peaks

Phonon anomalies and lattice dynamics in superconducting oxychlorides Ca2−x_{2-x}CuO2_2Cl

We present a comprehensive study of the phonon dispersion in an underdoped, superconducting Ca$_{2-x}$CuO$_2$Cl$_2$ crystal. We interpret the results using lattice dynamical calculations based on a shell model, and we compare the results, to other hole-doped cuprates, in particular to the ones isomorphic to La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). We found that an anomalous dip in the Cu-O bond stretching dispersion develops in oxychlorides with a simultaneous marked broadening of the mode. The broadening is maximum at $\approx (\pi / (2a) ~ 0 ~ 0)$ that corresponds to the charge-modulations propagation vector. Our analysis also suggests that screening effects in calculations may cause an apparent cosine-shaped bending of the Cu-O bond-stretching dispersion along both the ($q$ 0 0) and ($q$ $q$ 0) directions, that is not observed on the data close to optimal doping. This observation suggests that the discrepancy between experimental data and \textit{ab-initio} calculations on this mode originates from an overestimation of the doping effects on the mode

Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity