^{1}

Monte Carlo (MC) technique is becoming a very effective simulation method for prediction and analysis of the grain growth kinetics at mesoscopic level. It should be noted that MC models have no real time of physical systems due to the probabilistic nature of this simulation technique. This leads to difficulties when converting simulated time, the Monte Carlo steps

Grain growth in polycrystals is achieved by decreasing the total number of grains as result of the small grains vanishing. As a grain grows, atoms just outside the boundary change the lattice arrangement from that of the neighboring shrinking grain to the growing grain. To model the microstructure evolution, there are some analytical theories that adequately describe grain growth kinetics [

In the limit where

With the progress of computational technology, significant progress has been made in quantitative understanding of grain growth by using computer simulation techniques, including Monte Carlo (MC) Potts model [

The lattice sites spacing Δ plays an important role in the Monte Carlo simulation of grain growth. In the present study, the relation between real time and simulated time

The variation of

2-Dimensional hexagonal lattice (cells) used in the calculation of the matrix area.

With the circular grains hypothesis, the matrix average areas are given by

By substituting (

Equation (

The grain growth Monte Carlo simulation is performed on a two-dimensional triangular lattice, where for each lattice site “

The grain growth MC algorithm is as follows:

Randomly select a lattice site “

Calculate the site energy

Assign to this site a new orientation

Calculate the new site energy

Calculate the net energy change

Reorientation is accepted with the transition probability (TP):

The number of reorientation attempts ^{2}) obtained by orientation imaging microscopy (

Grain structure of the primary matrix analyzed by

From MC simulation results, Figure

Matrix mean sites number

Variation of real time versus simulated time

Equation (

Mean sites number

The lattice sites spacing Δ plays an important role in the Monte Carlo simulation of grain growth. To see the influence of Δ on the real time, three cases will be considered for the second simulation:

Variation of

Variation of real time versus simulated time

Influence of Δ on microstructural evolution after

In addition to the problem of the real time conversion, the mechanism of the temperature influence on the calculated results using MC simulation for grain growth is not well understood. The influence of temperature can be introduced usually in the Monte Carlo simulation through the transition probability in reorientation attempts (see (

While using relation (

Variation of the real time versus the simulated time

Square matrix mean-radius variation versus real time as function of temperature.

Simulated grain structure for 6 min at (a)

In addition to the problem of the correspondence between the simulated time

The author declares that there are no conflicts of interest.