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Browsing Instituto de Física by Author "Nelphy de la Cruz"
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- ItemDFT based kinetic Monte Carlo study of metal Surface Growth: Comparison of a restricted and an unrestricted diffusion model(2024-06-05) Nelphy de la CruzThe growth behavior of Cr and W surfaces using kinetic Monte Carlo (KMC) simulations based on Density-Functional Theory (DFT) is presented in this study. Three models, a growth model with random deposition and no diffusion, a growth model with restricted diffusion and a growth model with unrestricted diffusion model, were compared to understand their influence on the predicted surface roughness and layer density. The impact of deposition rate and temperature on surface growth for both metals were analyzed. For deposition rate studies, five different rates (0.01 ML/s, 0.1 ML/s, 1.0 ML/s, 10.0 ML/s, and 100 ML/s) were considered at 550 K for Cr and W respectively. The effect of temperature on roughness was also studied employing various temperatures from 300 K to 1100 K for both metals and under the two different evolution models. The results show that the unrestricted diffusion model exhibits higher roughness compared to the restricted model for both metals. The restricted model shows a stable region of roughness, whereas the unrestricted model shows a continuous increase in roughness throughout the simulation. Furthermore, layer density analysis revealed that temperature affects the filling of lower monolayers. Finally, dynamic exponents β and α for each studied model were calculated and discussed. The results highlight the influence of diffusion models, deposition rate and temperature on surface, roughness, and layer density.
- ItemDimer site-bond percolation on a triangular lattice(2017-02-06) Nelphy de la CruzA generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means of numerical simulations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as $S{\cap}^{}B$ and $S{\cup}^{}B$ ) have been considered. In $S{\cap}^{}B$ ($S{\cup}^{}B$ ), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. Numerical data, supplemented by analysis using finite-size scaling theory, were used to determine (i) the complete phase diagram of the system (phase boundary between the percolating and nonpercolating regions), and (ii) the values of the critical exponents (and universality) characterizing the phase transition occurring in the system.
- ItemInverse percolation by removing straight semirigid rods from bilayer square lattices(2023-06-22) Fabio Pimentel; Nelphy de la CruzNumerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse percolation by removing semirigid rods from a L×L square lattice that contains two layers (and M=L×L×2 sites). The process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by removing groups of k consecutive monomers according to a generalized random sequential adsorption mechanism. The study is conducted by following the behavior of two critical concentrations with size k: (1) jamming coverage θj,k, which represents the concentration of occupied sites at which the jamming state is reached, and (2) inverse percolation threshold θc,k, which corresponds to the maximum concentration of occupied sites for which connectivity disappears. The obtained results indicate that (1) the jamming coverage exhibits an increasing dependence on the size k—it rapidly increases for small values of k and asymptotically converges towards a definite value for infinitely large k sizes θj,k→∞≈0.2701—and (2) the inverse percolation threshold is a decreasing function of k in the range 1≤k≤17. For k≥18, all jammed configurations are percolating states (the lattice remains connected even when the highest allowed concentration of removed sites is reached) and, consequently, there is no nonpercolating phase. This finding contrasts with the results obtained in literature for a complementary problem, where straight rigid k-mers are randomly and irreversibly deposited on a square lattice forming two layers. In this case, percolating and nonpercolating phases extend to infinity in the space of the parameter k and the model presents percolation transition for the whole range of k. The results obtained in the present study were also compared with those reported for the case of inverse percolation by removal of rigid linear k-mers from a square monolayer. The differences observed between monolayer and bilayer problems were discussed in terms of vulnerability and network robustness. Finally, the accurate determination of the critical exponents ν, β, and γ reveals that the percolation phase transition involved in the system has the same universality class as the standard percolation problem.
- ItemIrreversible bilayer adsorption of straight semirigid rods on two-dimensional square lattices: Jamming and percolation properties.(2020-07-30) Nelphy de la CruzSe han realizado simulaciones numéricas y análisis de escalado de tamaño finito para estudiar el comportamiento de interferencia y percolación de varillas semirígidas rectas adsorbidas en celosías cuadradas bidimensionales. Los objetos depositantes pueden ser adsorbidos en la superficie formando dos capas. El llenado de la red se lleva a cabo siguiendo un mecanismo de adsorción secuencial aleatoria generalizada (RSA). En cada paso elemental, (i) se elige aleatoriamente un conjunto de sitios vecinos más cercanos consecutivos (alineados a lo largo de uno de los dos ejes de red) y (ii) si cada sitio seleccionado está vacío u ocupado por una unidad k-mer en la primera capa, entonces se deposita un nuevo en la red. De lo contrario, el intento es rechazado. El proceso comienza con una red inicialmente vacía y continúa hasta que se alcanza el estado de interferencia y no se pueden depositar más objetos debido a la ausencia de grupos de sitios vacíos de tamaño y forma apropiados. Se investiga un amplio rango de valores de (2). El estudio de las propiedades cinéticas del sistema muestra que (1) la cobertura de interferencia es una función decreciente con creciente, con el valor límite para -mers y (2) el exponente de interferencia permanece cerca de 1, independientemente del tamaño k considerado. Estos hallazgos se discuten en términos de la dimensionalidad de la red y el número de sitios disponibles para la adsorción. También se determina la dependencia del umbral de percolación en función de k, con, donde es el valor del umbral de percolación por infinitamente largos, B, y. Este comportamiento decreciente monótono es completamente diferente del observado para el problema estándar de varillas rectas en celosías cuadradas, donde el umbral de percolación muestra una dependencia no monotónica del tamaño. Las diferencias entre los resultados obtenidos de las fases bicapa y monocapa se explican sobre la base de los solapamientos transversales entre varillas que se producen en el problema de la bicapa. Este efecto (que llamamos un "efecto de reticulación"), sus consecuencias en la cinética de llenado y sus implicaciones en el campo de la conductividad de los compuestos llenos de partículas alargadas (o fibras) se discuten en detalle. Finalmente, la determinación precisa de los exponentes críticos ν e indica que, aunque el aumento en el ancho de la capa depositada afecta drásticamente el comportamiento del umbral de percolación con y otras propiedades críticas (como los puntos de cruce de las funciones de probabilidad de percolación), no altera la naturaleza de la transición de percolación que ocurre en el sistema. En consecuencia, el modelo bicapa pertenece a la misma clase de universalidad que el modelo de percolación estándar bidimensional.
- ItemIrreversible multilayer of semi-rigid k-mersdeposite don one-dimensional lattice.(2020-07-02) Nelphy de la CruzIrreversible multilayer adsorption of semirigid 𝑘-mers on one-dimensional lattices of size 𝐿 is studied by numerical simulations complemented by exhaustive enumeration of configurations for small lattices. The deposition process is modeled by using a random sequential adsorption algorithm, generalized to the case of multilayer adsorption. The paper concentrates on measuring the jamming coverage for different values of 𝑘-mer size and number of layers 𝑛. The bilayer problem (𝑛≤2) is exhaustively analyzed, and the resulting tendencies are validated by the exact enumeration techniques. Then, the study is extended to an increasing number of layers, which is one of the noteworthy parts of this work. The obtained results allow the following: (i) to characterize the structure of the adsorbed phase for the multilayer problem. As 𝑛 increases, the (1+1)-dimensional adsorbed phase tends to be a “partial wall” consisting of “towers” (or columns) of width 𝑘, separated by valleys of empty sites. The length of these valleys diminishes with increasing 𝑘; (ii) to establish that this is an in-registry adsorption process, where each incoming 𝑘-mer is likely to be adsorbed exactly onto an already adsorbed one. With respect to percolation, our calculations show that the percolation probability vanishes as 𝐿 increases, being zero in the limit 𝐿→∞. Finally, the value of the jamming critical exponent 𝜈𝑗 is reported here for multilayer adsorption: 𝜈𝑗 remains close to 2 regardless of the considered values of 𝑘 and 𝑛. This finding is discussed in terms of the lattice dimensionality.
- ItemStandard and inverse site percolation of triangular tiles on triangular lattices: Isotropic and perfectly oriented deposition and removal(2024-03-05) Nelphy de la Cruz"Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of triangular tiles of side 𝑘 (𝑘-tiles) on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, 𝑘-tiles are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing 𝑘-tiles [composed by 𝑘(𝑘+1)/2 monomers] from the lattice. Two schemes are used for the depositing and removing process: the isotropic scheme, where the deposition (removal) of the objects occurs with the same probability in any lattice direction; and the anisotropic (perfectly oriented or nematic) scheme, where one lattice direction is privileged for depositing (removing) the tiles. The study is conducted by following the behavior of four critical concentrations with the size 𝑘: (𝑖) [(𝑖𝑖)] standard isotropic (oriented) percolation threshold 𝜃𝑐,𝑘 (𝜗𝑐,𝑘), which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. 𝜃𝑐,𝑘 (𝜗𝑐,𝑘) is reached by isotropic (oriented) deposition of 𝑘-tiles on an initially empty lattice; and (𝑖𝑖𝑖) [(𝑖𝑣)] inverse isotropic (oriented) percolation threshold 𝜃𝑖 𝑐,𝑘 (𝜗𝑖 𝑐,𝑘), which corresponds to the maximum concentration of occupied sites for which connectivity disappears. 𝜃𝑖 𝑐,𝑘 (𝜗𝑖 𝑐,𝑘) is reached after removing isotropic (completely aligned) 𝑘-tiles from an initially fully occupied lattice. The obtained results indicate that (1)𝜃𝑐,𝑘 (𝜃𝑖 𝑐,𝑘) is an increasing (decreasing) function of 𝑘 in the range 1≤𝑘≤6. For 𝑘≥7, all jammed configurations are nonpercolating (percolating) states and, consequently, the percolation phase transition disappears. (2)𝜗𝑐,𝑘 (𝜗𝑖 𝑐,𝑘) show a behavior qualitatively similar to that observed for isotropic deposition. In this case, the minimum value of 𝑘 at which the phase transition disappears is 𝑘=5. (3) For both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line 𝜃(𝜗)=0.5. Thus, a complementary property is found 𝜃𝑐,𝑘+𝜃𝑖 𝑐,𝑘=1 (and 𝜗𝑐,𝑘+𝜗𝑖 𝑐,𝑘=1), which has not been observed in other regular lattices. (4) Finally, in all cases, the jamming exponent 𝜈𝑗 was measured, being 𝜈𝑗=1 regardless of the orientation (isotropic or nematic) or the size 𝑘 considered. In addition, the accurate determination of the critical exponents 𝜈, 𝛽, and 𝛾 reveals that the percolation phase transition involved in the system, which occurs for 𝑘 varying between one and five (three) for isotropic (nematic) deposition scheme, has the same universality class as the standard percolation problem."
- ItemSurface Growth during random and irreversible multilayer deposition of straight semirigid rods,(2021-09-02) Nelphy de la Cruzrandom sequential adsorption mechanism where the depositing objects can be adsorbed on the surface forming multilayers. The results of our simulations show that the roughness evolves in time following two different behaviors: an “homogeneous growth regime” at initial times, where the heights of the columns homogeneously increase, and a “segmented growth regime” at long times, where the adsorbed phase is segmented in actively growing columns and inactive nongrowing sites. Under these conditions, the surface growth generated by the deposition of particles of different sizes is studied. At long times, the roughness of the systems increases linearly with time, with growth exponent β=1, at variance with a random deposition of monomers which presents a sublinear behavior (β=1/2). The linear behavior is due to the segmented growth process, as we show using a simple analytical model.