In this work, the evolution of a tridimensional (3D) spherical crystal with mobile particles using a Monte Carlo algorithm is presented. The mean radius R of spherical crystal without particles changes according to the law: R2 = -4kt + Ro2, where Ro is the initial radius and k is a crystal constant. However, this law is modified when mobile particles are included. The effect of two types of mobile particles on the grain boundary migration of a spherical grain was also studied. One type of particle remained located in the middle of the grain boundary once it was incorporated (CT), and the other type of particle remained at the grain boundary without having any particular location (NC). It could be seen that the CT particle slowed down more the grain boundary migration than the NC particles. It was also found that the rate of reduction of the grain area is inversely proportional to the concentration of CT particles in the grain boundary for all the CT particles concentrations. Finally, it was established that the grain reaches a limit radius for CT particles which is related to the amount of particles that can be accommodated in the grain boundary.
R e c i b i d o : 1 4 / 0 5 / 1 7 ; a c e p t a d o : 1 9 / 0 4 / 1 8En este trabajo se presenta un modelo de simulación de crecimiento de grano con partículas móviles en tres dimensiones usando el método Monte Carlo. Se estudió el efecto de la concentración y el tamaño de las partículas sobre el tamaño de grano. En general, se pudo observar la migración de las partículas hacia los bordes de grano y el frenado que las mismas producen sobre el movimiento de los límites de grano. También se observó a tiempos largos un efecto de liberación de los bordes de grano respecto a las partículas. Se determinó el radio crítico donde los granos se frenan para cada concentración y cada tamaño de partícula. Finalmente, se presenta la relación entre el radio crítico, el tamaño de las partículas y concentración de las mismas. Se concluyó que el radio crítico es en general igual al radio de la esfera equivalente al volumen entre las partículas.
RESUMENEn este trabajo se presenta un modelo de simulación de crecimiento de grano con partículas móviles en tres dimensiones usando el método Monte Carlo. Se estudió el efecto de la concentración y el tamaño de las partículas sobre el tamaño de grano. En general, se pudo observar la migración de las partículas hacia los bordes de grano y el frenado que las mismas producen sobre el movimiento de los límites de grano. También se observó a tiempos largos un efecto de liberación de los bordes de grano respecto a las partículas. Se determinó el radio crítico donde los granos se frenan para cada concentración y cada tamaño de partícula. Finalmente, se presenta la relación entre el radio crítico, el tamaño de las partículas y concentración de las mismas. Se concluyó que el radio crítico es en general igual al radio de la esfera equivalente al volumen entre las partículas. Palabras clave: Monte Carlo, Crecimiento de Grano, Partículas móviles, Partículas de Segunda Fase, Efecto Zener. ABSTRACTIn this paper we present a simulation model of grain growth with moving particles in three dimensions using the Monte Carlo method. The effect of concentration and particle size on grain size was studied. In general, it was possible to observe the migration of the particles towards the grain boundaries and the braking that they produce on the movement of the grain boundaries. An effect of releasing the grain boundaries from the particles was also observed at long times. The critical radius, where the grains were braked for each concentration and particle size, was determined. Finally, the relation between the critical radius, the particle size and the concentration of the particles is presented. It was concluded that the critical radius is generally equal to the radius of the sphere equivalent to the volume between the particles. Keywords: Monte Carlo, Grain Growth, Moving Particles, Second Phase Particles, Zener Effect. INTRODUCCIÓNEl método de Monte Carlo (MC) ha sido utilizado para simular numéricamente el crecimiento de grano (CG) en muestras policristalinas bidimensionales (2D) [1,2]. YU y ESCHE [3] presentaron un análisis cinético y topológico del MC en CG en muestras policristalinas en tres dimensiones (3D) sin partículas.Con el mismo método se estudiaron efectos de las impurezas inmóviles [4] y móviles [5] sobre muestras 2D y efectos de las impurezas inmóviles sobre muestras policristalinas tridimensionales [6].El CG con partículas de segunda fase dispersa es de interés en glaciología. El CG en muestras de hielo polar y su relación con los contaminantes se encuentra ligado al clima del pasado y su investigación es relevante hoy día para conocer el comportamiento del clima [7]. En los hielo polares se encuentran, en
The surface of a monocrystalline ice sample was observed at −5 ◦C (268 K). For which it was superficially polished and allowed to evolve in the presence of activated silica gel for three hours. The evolution of a depression was studied using three-dimensional micrographs obtained with an Olympus OLS4000 LEXT confocal microscope. A predominance of surface diffusion transport was found in the evolution of the depression. This is based both on the value obtained for the surface diffusion coefficient, as well as on the values found for the exponents corresponding to the evolution of the depth of the well and its width.
The migration of a grain triple junction was studied on ice pure samples with bubbles at -2°C for almost 3 h. This work studies the interaction between Grain Boundary (GB) and bubbles. The evolution of the triple junction was recorded from successive photographs obtained from a LEICA® optical microscope. Simultaneously, numerical simulations of grain triple junction with mobile bubbles were carried out using Monte Carlo method with the following conditions: The bubbles in the bulk were kept immobile and those in the GB were allowed to move. In addition, mobile bubbles were forced to stay inside the GB. The simulations show that bubbles slow down the movement of the GB and of the triple junction. What’s more, the simulated triple junction obtained fits very well the experimental triple junction geometry, and the GB diffusivity values obtained coincide with those measured experimentally at the same temperature and reported by other authors. Finally, the drag effect of the mobile bubbles on the GB migration was verified.
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