Monte Carlo Simulation For The Microstructure Development During The Sintering Process

Powder metallurgy is a kind of important process to fabricate the advanced materials and products. It has lots of merits, such as the effective modification to the constituent and microstructure in materials, the fabrication of the materials with non-equilibrium status, the composition of many types of materials, and the easy realization of near net shape and automatic production. Sintering is one of the significant links in powder metallurgy process, since it determines the modification of microstructure and further the final operational performance of the powder metallurgy materials and products. The trial and error method based on experience is usually employed to establish and optimize the sintering process, which is onerous, time-consuming, and difficult to trace the development of microstructure (such as the growth of matrix grain and the shrinkage of pores) with real time. Computer simulation techniques attract much favorable attention recently, because they can give reference for the establishment and optimization of sintering schedule through the illustration, visualization and quantification of the dynamic behavior of sintering microstructure development. Among the computer simulation techniques, Monte Carlo method is very effective to simulate the sintering process, due to the easy simulation realization and program design, the relatively fast simulation speed, and the ability to directly represent the sintering microstructure development by the computer graphic technology.The key factor of Monte Carlo method to realize the sintering simulation is to establish the simulation rules which influence the reliability of simulation results significantly, especially for the mass diffusion and transportation behaviors. In this paper, the simulation rules were established according to physical and chemical essences of the mass transition in grain boundary and then grain growth during the later densification period of solid state sintering (approximately treated as the completely compact body), the dissolution-diffusion-precipitation behavior during the liquid phase sintering, and the grain growth-pore migration - vacancy annihilation during the middle and late period of solid state sintering. The above-mentioned three kinds of microstructure development processes were simulated by the Monte Carlo method using these simulation rules.Considering that an energy barrier should be conquered to realize the mass transition in the grain boundary during the real grain growth process, the Monte Carlo method was modified by introducing the energy barrier for mass transition into the evaluation of mass transition probability to simulate the normal grain growth. The aim of modification was to improve the physical significance of simulation. The simulation results show that the simulated grain growth exponent is 0.472-0.493 by the variation of simulation conditions, which is close to the theoretical value of 0.5 and in accord with the grain growth kinetics theory. The simulation results were verified by the experiment results obtained through sintering the lead magnesium niobate ceramic to form approximately compact bodies. It shows that the simulation results of grain morphology development and grain boundary topological characteristic are in keeping with the rules of real grain growth process.The simulation rules for the formation, diffusion and precipitation of solutes were established to simulate the dissolution of single circle particle in the liquid phase by the Monte Carlo method. The simulation results show that the increased particle dissolution degree and solute concentration up to be saturated in the liquid phase with the prolongation of simulation time, leading to the tendency of particle morphology to attain the equilibrium status after the simulation realization of dissolution process. The dissolution rate is promoted by increasing the simulation temperature, which decreases the time to attain the saturation in the liquid phase and increases the saturation concentration. The simulation can also realize that the smaller particle has the higher dissolution activity. Through simulating the dissolution of the particles with several initial radius up to attain the dissolving equilibrium in the liquid phase, it shows the the as-resulted equilibrium particle size and saturation concentration have the Gibbs-Thomson relation. The above-mentioned simulation results are in accord with the real dissolution process. The Monte Carlo method was used to simulate the particle growth behavior based on the Ostwald ripening mechanism during the liquid phase sintering process. The simulation ruled used in the simulation of the dissolution of single circle particle in the liquid phase was referred. The particle lattice and solute lattice were defined according to the position status of solid lattices in the simulation system. During the simulation, it was stipulated that the particle lattice must be switched to the solute lattice during the simulation of the dissolution of particle, and only the solute lattice may be switched to the particle lattice during the simulation of precipitation. The simulation results show that the particle growth exponent of 0.315?0.322 is obtained, which is almost independent on the simulation conditions of liquid phase content and temperature. These values are in agreement with the predictions of Ostwald ripening theories that predict power law behavior for grain growth with an exponent of 1/3 for diffusion-controlled kinetics. The increments of liquid phase content and simulation temperature promote the effective exchange of status between a pair of neighbor solid lattice - liquid lattice, leading to accelerate the dissolution - diffusion - precipitation process and decrement of interfacial energy. As a result, the faster particle growth behavior can be reflected. The above-mentioned simulation results were certified by the sintering experiments of NiFe2O4 ceramic with Cu/Ni as the liquid phase.The shrinkage behavior of sintering matrix in the middle and late stage of solid state sintering was simulated by the Monte Carlo method. During the simulation, the simulation rules were established according to the matrix grain growth, pore migration and vacancy annihilation. The relation between the simulation time and pore shrinkage rate were established after the simulation realization of the shrinkage of circle pore in the flat grain boundary between two grains. And the pore shrinkage behavior in this sintering model was also analyzed theoretically based on the mass diffusion flux. The simulation time-pore shrinkage rate obtained by simulating is confirmed closely to that obtained by theoretically modeling and analyzing. Through considering an energy barrier that should be conquered to realize the mass transition in the interface into the calculation of Boltzman Probability, the simulation result of enhanced grain growth rate after increasing the simulation temperature is obtained. After increasing the kT values, the Boltzman Probability is increased accordingly, leading to promote the simulation realization of grain growth, pore migration, vacancy annihilation through switching the pore lattice to the vacancy lattice, and finally the pore shrinkage simultaneously. The increment of grain boundary energy results in the enhanced grain boundary migration rate and then the larger grain size after treating with the same simulation time as shown in the simulation results. But the pores in the grains increases, which are hard to realize the shrinkage and elimination and then lead to the lower matrix shrinkage degree. After increasing the surface energy, the simulated results show the prominently enhance degree of sintering shrinkage and elimination of pores. Since that the pores that hinder the grain boundary migration decrease, the rates of grain boundary migration and grain growth both enhance. The above-mentioned simulation results of microstructure development of solid state sintering process obtained by changing the simulation temperature and interfacial energy status are in accord with the real solid state sintering phenomenon and laws. The above-mentioned simulation results were certified by the sintering systems of Y2O3,17-4 PH stainless steel, Al2O3 and molybdenum.