![[MAP Logo]](../../maplogo1.gif)
Professor Yoshiyuki Saito
Waseda University
Department of Materials Science and Engineering
3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 Japan
yoshi@dice.cache.waseda.ac.jp
Simulation of grain growth kinetics using a Monte Carlo method in two dimensions. This is a new algorithm which has the advantage that it prevents grains of the same orientation from coalescing.
| Language: | FORTRAN |
| Product form: | Source code |
The program reads inputs from a file, in this case called Graingrowth.montecarlo.dat which contains the following: 256 256 200 1459873 32 2048 1.00 3 The first and second numbers specify the system size which is the number of cells in the two-dimensional Monte Carlo simulation. The third number is the time in Monte Carlo units. The fourth number is the initial random number which should be a prime number. The fifth number sets the total number of orientations of the grains in the simulation. The sixth number is the initial number of grains. The seventh number sets the anisotropy of the grain boundary energy (a value of unity represents isotropy, and values less than unity but greater than zero represent an orientation dependence of interface energy). The final number need not be altered at all; it is a file control parameter.
The Monte Carlo simulation method is now widely applied to materials science and engineering. This program deals with grain growth kinetics in two-dimensions, with the simulation of interface motion based on the Potts model. As an initial microstructure, an orientation between 1 to Q is assigned to each lattice site at random. The evolution of the grain structure then occurs during the Monte Carlo iterations. It is possible to obtain both the mean grain size and the grain size distribution.
These are read from the file Graingrowth.montecarlo.data which has a single row as follows :-
Output is to three ASCII files, fort.15, fort.16 and fort.17. See program results (below) for format.
None.
See [2], which has a comparison between calculations and experimental observations.
A three-dimensional simulation will be available in the near future.
See full program
256 256 200 1459873 32 2048 1.00 3
There are three output files created, fort.15, fort.16 and fort.17
File fort.15 has two columns, the first representing the Monte Carlo time, and the second, the number of grains remaining :-
1 1552
2 1552
3 1552
4 1552
5 1552
6 1552
7 1552
8 1552
9 1552
10 1552
11 1552
12 1552
13 1552
14 1552
15 1552
16 1552
17 1552
18 1552
19 1552
20 1552
21 1552
22 1552
23 1552
24 1552
25 1552
26 1552
27 1552
28 1552
29 1552
30 1552
31 1552
32 1552
33 1552
34 1552
35 1552
36 1552
37 1552
38 1551
39 1550
40 1550
41 1550
42 1550
43 1550
44 1550
45 1550
46 1549
47 1549
48 1549
49 1549
50 1549
100 1534
150 1494
200 1444
File fort.16 has columns which represent 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000 Monte Carlo time steps. The number of columns may be less than 10 if the simulation is stopped at an earlier end point (less than 10000). Each row represents the fraction of grains which have the same number of corners as the row number (i.e., row 5 represents pentagons and row 10 decagons) :-
0.00 0.00 0.06 0.00 0.21
0.32 0.52 0.52 1.04 0.97
3.35 3.93 3.74 4.17 4.57
13.72 12.18 12.46 12.39 13.30
21.78 21.46 21.37 20.66 19.88
24.74 25.00 25.18 23.14 22.02
18.04 19.78 18.27 18.64 17.80
11.28 10.18 10.65 12.19 12.60
4.64 4.96 5.81 5.08 5.61
1.74 1.68 1.36 2.28 2.22
0.32 0.19 0.52 0.33 0.69
0.06 0.13 0.06 0.07 0.14
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
File fort.17 has columns which represent 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000 Monte Carlo time steps. The number of columns may be less than 10 if the simulation is stopped at an earlier end point (less than 10000). Row number 11 in each case gives the fraction of grains of average size. Row number 21 gives the fraction of grains of twice the average size. The other rows can be interpreted on the same rationale.
0.06 0.39 0.77 2.09 3.88
0.90 1.68 2.13 2.41 3.19
3.41 2.84 3.10 5.08 5.54
4.57 5.28 5.42 4.63 3.88
7.02 6.77 5.75 6.39 7.34
8.63 8.63 9.62 7.69 5.75
8.63 7.54 7.62 7.30 7.27
6.57 7.35 7.68 6.19 5.47
8.38 7.09 6.58 6.91 6.86
7.22 8.38 6.58 5.87 5.40
8.76 8.18 8.07 7.24 6.86
5.35 4.77 5.62 5.61 5.26
5.54 5.61 4.65 4.82 5.26
5.35 5.28 4.13 4.24 3.05
3.09 3.61 4.84 3.26 3.53
3.80 3.74 3.36 4.11 3.12
2.19 2.06 2.39 2.48 3.67
2.00 1.87 1.87 2.35 2.49
1.55 1.68 1.61 1.89 2.49
1.29 1.48 1.87 1.89 1.66
1.55 1.22 1.68 1.76 1.32
0.84 1.03 0.65 1.04 1.66
0.90 1.03 0.84 0.91 0.90
0.77 0.71 0.90 0.78 0.90
0.39 0.52 0.39 0.78 0.90
0.26 0.26 0.58 0.72 0.42
0.13 0.13 0.32 0.07 0.48
0.13 0.26 0.19 0.46 0.14
0.13 0.06 0.06 0.07 0.21
0.06 0.19 0.13 0.13 0.14
0.13 0.00 0.13 0.20 0.28
0.06 0.00 0.06 0.13 0.14
0.06 0.13 0.06 0.13 0.21
0.00 0.00 0.06 0.07 0.00
0.06 0.00 0.00 0.00 0.07
0.06 0.13 0.13 0.13 0.07
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.07 0.07
0.13 0.06 0.00 0.00 0.07
0.00 0.06 0.06 0.00 0.00
0.00 0.00 0.06 0.07 0.07
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.07 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
None.
Monte Carlo Simulation Grain Growth Kinetics
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
MAP Website administration / map@msm.cam.ac.uk