arXiv subjects

Rafael Ramirez

Publications and source records attributed to Rafael Ramirez.

At least 37 records · Page 2Linked to original sources

arXiv2015

Path-integral simulation of ice VII: Pressure and temperature effects

Effects of pressure and temperature on structural and thermodynamic properties of ice VII have been studied by using path-integral molecular dynamics (PIMD) simulations. Temperatures between 25 and 450 K, as well as pressures up to 12 GPa were considered. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. We analyze the pressure dependence of the molar volume, bulk modulus, interatomic distances, kinetic energy, and atomic delocalization at various temperatures. Results of PIMD simulations are compared with those derived from a quasi-harmonic approximation (QHA) of vibrational modes, which helps to assess the importance of anharmonic effects, as well as the influence of the different modes on the properties of ice VII. The accuracy of the QHA for describing this high-pressure phase decreases for rising temperature, but this approximation becomes more reliable as pressure grows, since anharmonicity becomes less relevant. Comparisons with low-pressure cubic ice are presented.

physics.chem-ph↗

arXiv2014

Configurational entropy of hydrogen-disordered ice polymorphs

The configurational entropy of several H-disordered ice polymorphs is calculated by means of a thermodynamic integration along a path between a totally H-disordered state and one fulfilling the Bernal-Fowler ice rules. A Monte Carlo procedure based on a simple energy model is used, so that the employed thermodynamic path drives the system from high temperatures to the low-temperature limit. This method turns out to be precise enough to give reliable values for the configurational entropy of different ice phases in the thermodynamic limit (number of molecules N --> infinity). The precision of the method is checked for the ice model on a two-dimensional square lattice. Results for the configurational entropy are given for H-disordered arrangements on several polymorphs, including ices Ih, Ic, II, III, IV, V, VI, and XII. The highest and lowest entropy values correspond to ices VI and XII, respectively, with a difference of 3.3\% between them. The dependence of the entropy on the ice structures has been rationalized by comparing it with structural parameters of the various polymorphs, such as the mean ring size. A particularly good correlation has been found between the configurational entropy and the connective constant derived from self-avoiding walks on the ice networks.

physics.chem-ph↗

arXiv2014

Path-integral simulation of solids

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

cond-mat.mtrl-sci↗

arXiv2013

Topological characterization of crystalline ice structures from coordination sequences

Topological properties of crystalline ice structures are studied by considering ring statistics, coordination sequences, and topological density of different ice phases. The coordination sequences (number of sites at topological distance k from a reference site) have been obtained by direct enumeration until at least 40 coordination spheres for different ice polymorphs. This allows us to study the asymptotic behavior of the mean number of sites in the k-th shell, M_k, for high values of k: M_k ~ a k^2, a being a structure-dependent parameter. Small departures from a strict parabolic dependence have been studied by considering first and second differences of the series {M_k} for each structure. The parameter a ranges from 2.00 for ice VI to 4.27 for ice XII, and is used to define a topological density for these solid phases of water. Correlations between such topological density and the actual volume of ice phases are discussed. Ices Ih and Ic are found to depart from the general trend in this correlation due to the large void space in their structures.

physics.chem-ph↗

arXiv2013

Configurational entropy of ice from thermodynamic integration

The configurational entropy of ice is calculated by thermodynamic integration from high to low temperatures. We use Monte Carlo simulations with a simple energy model which reproduces the Bernal-Fowler ice rules. This procedure is found to be precise enough to give reliable values for the residual entropy s_th of different ice phases in the thermodynamic limit. First, we check it for a two-dimensional ice model. Second, we calculate s_th for ice Ih, and compare our result with those previously given in the literature. Third, we obtain s_th for ice VI, for which we find a value clearly higher than for ice Ih.

physics.chem-ph↗

arXiv2012

High-density amorphous ice: A path-integral simulation

Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (T = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O--H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened respect to their classical expectancy. The bulk modulus, B, is found to rise linearly with the pressure, with a slope dB/dP = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.

physics.chem-ph↗

arXiv2012

Path-integral simulation of ice Ih: The effect of pressure

The effect of pressure on structural and thermodynamic properties of ice Ih has been studied by means of path-integral molecular dynamics simulations at temperatures between 50 and 300 K. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Positive (compression) and negative (tension) pressures have been considered, which allowed us to approach the limits for the mechanical stability of this solid water phase. We have studied the pressure dependence of the crystal volume, bulk modulus, interatomic distances, atomic delocalization, and kinetic energy. The spinodal point at both negative and positive pressures is derived from the vanishing of the bulk modulus. For P < 0, the spinodal pressure changes from -1.38 to -0.73 GPa in the range from 50 to 300 K. At positive pressure the spinodal is associated to ice amorphization, and at low temperatures is found between 1.1 and 1.3 GPa. Quantum nuclear effects cause a reduction of the metastability region of ice Ih.

cond-mat.mtrl-sci↗

arXiv2011

Diffusion of hydrogen in graphite: A molecular dynamics simulation

Diffusion of atomic and molecular hydrogen in the interstitial space between graphite sheets has been studied by molecular dynamics simulations. Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. Atomic hydrogen is found to be bounded to C atoms, and its diffusion consists in jumping from a C atom to a neighboring one, with an activation energy of about 0.4 eV. Molecular hydrogen is less attached to the host sheets and diffuses faster than isolated H. At temperatures lower than 500 K, H_2 diffuses with an activation energy of 89 meV, whereas at higher T its diffusion is enhanced by longer jumps of the molecule as well as by correlations between successive hops, yielding an effective activation energy of 190 meV.

cond-mat.mtrl-sci↗

arXiv2011

Molecular hydrogen in graphite: A path-integral simulation

Molecular hydrogen in the bulk of graphite has been studied by path-integral molecular dynamics simulations. Finite-temperature properties of H_2 molecules adsorbed between graphite layers were analyzed in the temperature range from 300 to 900 K. The interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. In the lowest-energy position, an H_2 molecule is found to be disposed parallel to the sheets plane. At finite temperatures, the molecule explores other orientations, but its rotation is partially hindered by the adjacent graphite layers. Vibrational frequencies were obtained from a linear-response approach, based on correlations of atom displacements. For the stretching vibration of the molecule, we find at 300 K a frequency omega_s = 3916 cm-1, more than 100 cm-1 lower than the frequency corresponding to an isolated H_2 molecule. Isotope effects have been studied by considering also deuterium and tritium molecules. For D_2 in graphite we obtained omega_s = 2816 cm-1}, i.e., an isotopic ratio omega_s(H) / omega_s(D) = 1.39.

cond-mat.mtrl-sci↗

arXiv2011

Isotope effects in ice Ih: A path-integral simulation

Ice Ih has been studied by path-integral molecular dynamics simulations, using the effective q-TIP4P/F potential model for flexible water. This has allowed us to analyze finite-temperature quantum effects in this solid phase from 25 to 300 K at ambient pressure. Among these effects we find a negative thermal expansion of ice at low temperatures, which does not appear in classical molecular dynamics simulations. The compressibility derived from volume fluctuations gives results in line with experimental data. We have analyzed isotope effects in ice Ih by considering normal, heavy, and tritiated water. In particular, we studied the effect of changing the isotopic mass of hydrogen on the kinetic energy and atomic delocalization in the crystal, as well as on structural properties such as interatomic distances and molar volume. For D$_2$O ice Ih at 100 K we obtained a decrease in molar volume and intramolecular O--H distance of 0.6% and 0.4%, respectively, as compared to H$_2$O ice.

cond-mat.mtrl-sci↗

arXiv2009

Molecular hydrogen in silicon: A path-integral simulation

Molecular hydrogen in silicon has been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 300 to 900 K. Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these impurities is found at the interstitial T site, with the hydrogen molecule rotating freely in the Si cage. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in the stretching vibration, omega_s, which is softened with respect to a harmonic approximation by about 300 cm^{-1}. The coupling between rotation and vibration causes an important decrease in omega_s for rising temperature.

cond-mat.mtrl-sci↗

arXiv2009

Vibrational properties and diffusion of hydrogen on graphene

Hydrogen and deuterium chemisorption on a single layer of graphene has been studied by path-integral molecular dynamics simulations. Finite-temperature properties of these point defects were analyzed in the range from 200 to 1500 K, by using a tight-binding potential fitted to density-functional calculations. On one side, vibrational properties of the adatoms are studied at their equilibrium positions, linked to C atoms. The vibrations display an appreciable anharmonicity, as derived from comparison between kinetic and potential energy, as well as between vibrational energy for hydrogen and deuterium. On the other side, adatom motion has been studied by quantum transition-state theory. At room temperature, quantum effects are found to enhance the hydrogen diffusivity on the graphene sheet by a factor of 20.

cond-mat.mtrl-sci↗

arXiv2009

Isotope effects on the lattice parameter of cubic SiC

Path-integral molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble have been carried out to study the dependence of the lattice parameter of 3C-SiC upon isotope mass. This computational method allows a quantitative and nonperturbative study of such anharmonic effect. Atomic nuclei were treated as quantum particles interacting via a tight-binding-type potential. At 300 K, the difference Delta a between lattice parameters of 3C-SiC crystals with 12C and 13C amounts to 2.1 x 10^{-4} A. The effect due to Si isotopes is smaller, and amounts to 3.5 x 10^{-5} A when replacing 28Si by 29Si. Results of the PIMD simulations are interpreted in terms of a quasiharmonic approximation for the lattice vibrations.

cond-mat.mtrl-sci↗

arXiv2009

Quantum contributions in the ice phases: the path to a new empirical model for water -- TIP4PQ/2005

With a view to a better understanding of the influence of atomic quantum delocalisation effects on the phase behaviour of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model, in conjunction with the rigid rotor propagator proposed by Muser and Berne [Phys. Rev. Lett. 77, 2638 (1996)]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example densities, structure and relative stabilities.

cond-mat.stat-mech↗

arXiv2009

Inverse Approach In The Study Of Ordinary Differential Equations

We extend the Eruguin result exposed in the paper "Construction of the whole set of ordinary differential equations with a given integral curve" published in 1952 and construct a differential system in $\Bbb{R}^N$ which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system of degree $n$ with one invariant irreducible algebraic curve $g(x,y)=0$. For this system we analyze the Darboux integrability, Poincare's problem and 16th's Hilbert problem for algebraic limit cycles.

math.DS↗

arXiv2009

Cartesian approach for constrained mechanical system with three degree of freedom

In the history of mechanics, there have been two points of view for studying mechanical systems: The Newtonian and the Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential equations in the $N$ dimensional configuration space $\textsc{Q}.$ In this paper we develop the Cartesian approach for mechanical systems with three degrees of freedom and with constraint which are linear with respect to velocity. The obtained results we apply to discuss the integrability of the geodesic flows on the surface in the three dimensional Euclidian space and to analyze the integrability of a heavy rigid body in the Suslov and the Veselov cases .

math.DS↗

arXiv2008

Path-integral molecular dynamics simulation of 3C-SiC

Molecular dynamics simulations of 3C-SiC have been performed as a function of pressure and temperature. These simulations treat both electrons and atomic nuclei by quantum mechanical methods. While the electronic structure of the solid is described by an efficient tight-binding Hamiltonian, the nuclei dynamics is treated by the path integral formulation of statistical mechanics. To assess the relevance of nuclear quantum effects, the results of quantum simulations are compared to others where either the Si nuclei, the C nuclei or both atomic nuclei are treated as classical particles. We find that the experimental thermal expansion of 3C-SiC is realistically reproduced by our simulations. The calculated bulk modulus of 3C-SiC and its pressure derivative at room temperature show also good agreement with the available experimental data. The effect of the electron-phonon interaction on the direct electronic gap of 3C-SiC has been calculated as a function of temperature and related to results obtained for bulk diamond and Si. Comparison to available experimental data shows satisfactory agreement, although we observe that the employed tight-binding model tends to overestimate the magnitude of the electron-phonon interaction. The effect of treating the atomic nuclei as classical particles on the direct gap of 3C-SiC has been assessed. We find that non-linear quantum effects related to the atomic masses are particularly relevant at temperatures below 250 K.

cond-mat.mtrl-sci↗

arXiv2007

Diffusion of muonium and hydrogen in diamond

Jump rates of muonium and hydrogen in diamond are calculated by quantum transition-state theory, based on the path-integral centroid formalism. This technique allows us to study the influence of vibrational mode quantization on the effective free-energy barriers Delta F for impurity diffusion, which are renormalized respect to the zero-temperature classical calculation. For the transition from a tetrahedral (T) site to a bond-center (BC) position, Delta F is larger for hydrogen than for muonium, and the opposite happens for the transition from BC to T. The calculated effective barriers decrease for rising temperature, except for the muonium transition from T to BC sites. Calculated jump rates are in good agreement to available muon spin rotation data.

cond-mat.mtrl-sci↗