---materialsim-grain-growth.nlogo

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height
height
3
501
45
1
1
atoms

TEXTBOX
12
17
205
35
(1) Simulation starting point

SLIDER
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149
464
182
annealing-temperature
annealing-temperature
0
100
0
1
1
%

BUTTON
237
308
392
347
measure grains now
grain-count
NIL
1
T
OBSERVER
T
NIL

PLOT
11
378
263
566
Grain Size (log-log)
log (time)
log (avg grain size)
0.0
200.0
0.0
1.0
true
false
PENS
"average-grain-size" 1.0 0 -16777216 false

MONITOR
268
437
376
486
Grain Size
average-grain-size
3
1

BUTTON
11
315
111
355
go
go
T
1
T
OBSERVER
NIL
NIL

SLIDER
235
185
463
218
fraction-element2
fraction-element2
0
10
0
1
1
NIL

BUTTON
9
36
200
69
start with random arrangement
makes-initial-box-random
NIL
1
T
OBSERVER
T
NIL

BUTTON
9
78
200
111
import image
import-image
NIL
1
T
OBSERVER
T
NIL

MONITOR
380
438
493
487
Log Grain Size
logaverage-grain-size
2
1

MONITOR
378
379
472
428
Log time
logtime
2
1

MONITOR
267
379
374
428
Simulation time
MCS
0
1

MONITOR
380
491
493
540
Growth exponent
grain-growth-exponent
2
1

TEXTBOX
11
295
150
313
(4) Run simulation

TEXTBOX
236
127
326
145
Special features

SLIDER
235
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423
298
measurement-frequency
measurement-frequency
1
100
1
1
1
NIL

TEXTBOX
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18
328
36
Simulation size

CHOOSER
10
135
111
180
atom-shape
atom-shape
"hex" "hexline" "thin-line" "line" "circ" "square" "spikes90" "default"
0

BUTTON
115
135
200
180
apply shape
ask turtles [set shape atom-shape]
NIL
1
T
OBSERVER
T
NIL

BUTTON
10
204
79
237
draw
turtle-draw
T
1
T
OBSERVER
T
NIL

BUTTON
10
243
79
286
erase all
erase-all
NIL
1
T
OBSERVER
T
NIL

SLIDER
82
204
200
237
brush-size
brush-size
1
6
4
1
1
NIL

TEXTBOX
11
185
101
203
(3) Draw grains

CHOOSER
82
242
200
287
draw-color
draw-color
45 55 85 105 15
0

TEXTBOX
237
244
367
262
Grain measurement

TEXTBOX
13
360
181
378
Grain size plot and calculations

TEXTBOX
10
115
186
133
(2) Change the shape of atoms

BUTTON
117
315
194
355
go once
go\n
NIL
1
T
OBSERVER
T
NIL

@#$#@#$#@
WHAT IS IT?
-----------
Most materials are not continuous arrangements of atoms, but rather composed of thousands or millions of microscopic crystals, known as grains.  This model shows how the configuration and sizes of these grains change over time.  Grain size is a very important characteristic for evaluating the mechanical properties of materials; it is exhaustively studied in metallurgy and materials science.

Usually this kind of study is made by careful analysis and comparison of pictures taken in microscopes, sometimes with the help of image analysis software.  Recently, as the processing power of computers has increased, a new and promising approach has been made possible: computer simulation of grain growth.  Anderson, Srolovitz et al. proposed the most widely known and employed theory for computer modeling and simulation of grain growth, using the Monte Carlo method.  Instead of considering the grains as spheres, and being obliged to make numerous geometrical approximations, Anderson proposed that the computer would simulate the behavior of each individual atom in the system. Each atom would follow a very simple rule: it will always try to have, in its immediate neighborhood, as many atoms as possible with the same orientation as it.

This model is part of the MaterialSim (Blikstein & Wilensky, 2004) curricular package. To learn more about MaterialSim, see http://ccl.northwestern.edu/materialsim/. 


HOW IT WORKS
------------
The basic algorithm of the simulation is simple: atoms are trying to be as stable as possible.  Their stability is based on the number of equal neighbors: the more equal neighbors (i.e. atoms with the same orientation) an atom has, the more stable it is.  If it has many different neighbors, it is unstable, and not likely to be in that position for long, because during the simulation atoms will try to relocate to more stable positions.  Therefore, the steps are:

1) Choose a random atom.
2) Calculate its present energy (which is correlated with the stability).  This calculation is done by simply counting the number of different neighbors.
3) Randomly choose a new orientation for the chosen atom, amongst the orientations of its neighbors.  We still don't know if that new attempted orientation will be maintained.  We have to calculate the energy in this new situation in order to know.
4) Calculate the free energy of the chosen element with the new, tentative orientation.  Again, we just count the number of different neighbors.
5) Comparison of the two values for free energy: the lowest value "wins", i.e., the less different neighbors an atom have, more stable it is.
6) Repeat steps 1-6.

The ANNEALING-TEMPERATURE slider controls the probability of maintaining an re-orientation which yields more instability.  The FRACTION-ELEMENT-2 slider defines the percentage of second-phase particles to be created when the user setups the simulation.  Those particles and not movable and are not subject to grain growth. Atoms see those particles as a different neighbor.

Note that the actual number of atoms is small compared to a real metal sample.  Also, real materials are three-dimensional, while this model is 2D. 


HOW TO USE IT
-------------
(1) Simulation starting point:
IMPORT IMAGE: Resets the simulation, and imports an image file in the JPG, BMP, GIF or PNG file formats.  The image will be automatically resized to fit into the view, but maintaining its original aspect ratio. Note that the image MUST HAVE THE SAME ASPECT RATIO AS THE VIEW. In other words, if the view is square, the image should be square as well. Prior to importing the image, it is recommended to clean it up using an image editing software (increase contrast, remove noise).  Try to experiment various combinations of values for the WIDTH and HEIGHT sliders, the view's size and the patch size to get the best results.
START WITH RANDOM ARRANGEMENT: Resets the simulation, and starts it with a random orientation for each atom.
GO-ONCE: Runs the simulation, one time step at a time.
GO: Runs the simulation continuously until either the GO button is pressed again, or just one grain survives.

(2) Change the shape of the atoms
The ATOM-SHAPE chooser has many different shapes, such as circle, hexagon, line, circle with spikes, thin line, and square.
After choosing the ATOM-SHAPE, click on APPLY to change the shape.  This can also be done during the simulation.

(3) Draw grains
You can draw grains with the mouse, using different brush sizes and colors.  The DRAW button activates drawing, the ERASE ALL button erases the screen and sets all the atoms to red, the BRUSH-SIZE slider controls the radius of the brush and the DRAW-COLOR chooser changes the numeric value of the drawing color.

(4) Run simulation
GO: runs the simulation continuously
GO ONCE: runs the simulation, one step at a time.

Simulation size
WIDTH: x (horizontal) dimension of the sample.
HEIGHT: y (vertical) dimension of the sample

Special features
ANNEALING-TEMP: changes the probability of non-favorable orientation flips to happen.  A 10% value, for instance, means that 10% of non-favorable flips will be maintained.  This mimics the effect of higher temperatures.
FRACTION-ELEMENT2: This slider controls the amount of dispersed second-phase particles throughout the sample. Those particles slow down or stop grain growth.

Grain measurement
MEASUREMENT-FREQUENCY: to increase the model's speed, the user can choose not to calculate grain size at every time step.  If grain size is calculated at every ten time units (20, 30, 40 etc.), the performance is slightly increased.  This only affects the plot and the monitors, but not the actual simulation.
MEASURE GRAINS NOW: if the MEASUREMENT-FREQUENCY is too large, and the user wants to evaluate grain size at a specific moment, this button can be used. Note that this does not alter the plot.

Plots and monitors
Grain Size (log-log): Grain size vs. time, in a log-log scale.  Under normal conditions (ANNEALING-TEMP = 0 and FRACTION-ELEMENT-2 = 0), this plot should be a straight line with an angular coefficient of approximately 0.5.
SIMULATION TIME and LOG TIME: time steps of the simulation so far (and its log)
GRAIN SIZE and LOG GRAIN SIZE: grain size (is atoms) and its log.
GROWTH EXPONENT: the angular coefficient of the GRAIN SIZE plot.  This number should approach 0.5 with ANNEALING-TEMP = 0 and FRACTION-ELEMENT2 = 0.


THINGS TO NOTICE
----------------
When you setup with a random orientation and run the simulation, notice that the speed of growth decreases with time.  Toward the end of the simulation, you might see just two or three grains that fight with each other for along time.  One will eventually prevail, but this logarithmic decrease of speed is an important characteristic of grain growth.  That is why the GRAIN SIZE plot is a straight line in a "log-log" scale.
Notice also that if you draw two grains, one concave and one convex, their boundary will tend to be a straight line, if you let the simulation run long enough.  Every curved boundary is unstable because many atoms at its interface will have more different than equal neighbors.