turtles-own
[
temp ;; specific turtle's temperature
turtle-neighbors ;; set of surrounding turtles
]
globals
[
ave-metal-temp ;; shows average temperature of all metal
num-frozen ;; keeps track of how many atoms are frozen
temp-range ;; for histogram
colors ;; used both to color turtles, and for histogra
pens ;; keeps track of all the histogram's pen names
]
to setup
clear-all
set colors sentence (white - 1) [cyan sky blue violet magenta red]
set pens []
set temp-range (init-metal-temp - melting-temp) / (length colors - 1)
ask patches with [(abs pycor >= box-width / 2) or
(abs pxcor >= box-width / 2)]
[ set pcolor white ]
;; fill room to desired percentage
ask patches
[
if ((fill-percentage > random-float 100) and (pcolor != white))
[
sprout 1
[
set shape "T"
set temp init-metal-temp
set turtle-neighbors (turtles at-points [[1 0] [0 1] [-1 0] [0 -1]])
set-color
]
]
]
set ave-metal-temp init-metal-temp
reset-ticks
end
to go
;; stop if all turtles are below melting temp
if (max ([temp] of turtles) < melting-temp)[ stop ]
;; otherwise...
set num-frozen 0
ask turtles [ move ]
ask turtles [ rotate ]
ask turtles [ cool-turtles ]
ask turtles [ set-color ]
set ave-metal-temp (mean [temp] of turtles)
tick
end
;; turtles procedure -- if metal is liquid, move to a randomly
;; selected neighboring patch that is not already occupied
to move
if (temp > melting-temp)
[
let move-choices neighbors4 with [(pcolor != white) and (not any? turtles-here)]
if any? move-choices
[
move-to one-of move-choices
]
]
end
;; turtle procedure -- if metal is liquid and it is next to a solid,
;; change its heading to that of the solid; otherwise, just rotate
;; randomly
to rotate
set turtle-neighbors turtles at-points [[1 0] [0 1] [-1 0] [0 -1]]
if (temp > melting-temp)
[
let frozen-neighbors (turtle-neighbors with [temp <= melting-temp])
ifelse (any? frozen-neighbors)
[ set heading ([heading] of (one-of frozen-neighbors)) ]
[ rt random-float 360 ]
]
end
;; turtle procedure -- sets turtle's temp to ave temp of all
;; neighboring turtles and patches added turtle's own temp in twice so
;; it changes more slowly
to cool-turtles
let walled-sides neighbors4 with [pcolor = white]
let total-temp ((sum [temp] of turtle-neighbors) +
(room-temp * (count walled-sides) + temp))
let total-num ((count turtle-neighbors) + (count walled-sides) + 1)
set temp (total-temp / total-num)
end
;; turtle procedure
to set-color
; create index ranging from 1 to 8 for all melting colors
let index (floor ((temp - melting-temp) / temp-range)) + 1
ifelse (index < 0 )
[
set color white - 1
set num-frozen (num-frozen + 1)
]
[
if index >= length colors
[ set index (length colors) - 1 ]
set color item index colors
]
end
; Copyright 2002 Uri Wilensky.
; See Info tab for full copyright and license.
@#$#@#$#@
GRAPHICS-WINDOW
339
10
769
461
17
17
12.0
1
10
1
1
1
0
0
0
1
-17
17
-17
17
1
1
1
ticks
30.0
BUTTON
241
85
304
118
go
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
BUTTON
208
42
267
75
NIL
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
SLIDER
9
42
161
75
room-temp
room-temp
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100
20
1
1
NIL
HORIZONTAL
SLIDER
9
85
161
118
init-metal-temp
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2500
1550
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1
NIL
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128
161
161
melting-temp
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1500
551
1
1
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MONITOR
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ave-metal-temp
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100
85
1
1
%
HORIZONTAL
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304
161
box-width
box-width
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33
33
2
1
atoms
HORIZONTAL
BUTTON
170
85
232
118
go once
go
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
SWITCH
17
187
141
220
histogram?
histogram?
0
1
-1000
PLOT
8
469
283
670
Average Metal Temperature
time
ave-metal-temp
0.0
100.0
20.0
1550.0
true
true
"set-plot-y-range room-temp init-metal-temp" "if not histogram? [ stop ]"
PENS
"ave-metal-temp" 1.0 0 -2674135 false "" "plot ave-metal-temp"
PLOT
288
469
501
670
Number Solidified
time
crystal quant.
0.0
100.0
0.0
625.0
true
false
"set-plot-y-range 0 count turtles" ""
PENS
"amount" 1.0 0 -16777216 false "" "plot num-frozen"
PLOT
507
469
755
670
Temperatures
colors
quantity
0.0
8.0
0.0
625.0
false
true
"set-plot-y-range 0 count turtles\nset-histogram-num-bars 1 + (length colors)\n\nlet bottom (round room-temp)\nlet top (round melting-temp)\nlet index 0\nforeach colors [\n create-temporary-plot-pen (word bottom \" - \" top)\n set-plot-pen-mode 1\n set-plot-pen-color ?\n set pens lput (word bottom \" - \" top) pens\n\n set index index + 1\n set bottom top\n set top (round ((index * temp-range) + melting-temp))\n]" ""
PENS
"quantity" 1.0 1 -2674135 false "" "if not histogram? [ stop ]\nlet index 0\nforeach colors [\n set-current-plot-pen (item index pens)\n plot-pen-reset\n if any? turtles with [color = ?]\n [ plotxy index count turtles with [color = ?] ]\n set index index + 1\n]"
@#$#@#$#@
## WHAT IS IT?
This model simulates the movement of metal atoms as a system crystallizes. It is very similar to the Crystallization Basic model, except here the atoms are free to move about. They randomly move in any direction that is not already occupied by something else, such as another atom or a wall. Therefore, in order to allow movement, there must be empty spaces between atoms. Initially these empty spaces, or voids, are randomly distributed, as they would be in a liquid metal.
The first atoms to crystallize have a random orientation. However, when a liquid atom about to crystallize is next to an already crystallized atom, the liquid atom orients itself with the solid atom, thus creating a crystal. As more and more atoms solidify, the crystals grow. Within each crystal, all the atoms are oriented with one another, but within the entire metal, all the crystals have random orientations. Each individual crystal is called a grain. When two crystals grow up next to each other, they form what is called a grain boundary.
When a metal is stressed, such as when it is pulled from both ends, deformations occur in the crystal structure. As more stress is applied, these deformations pass through the crystal structure, allowing the metal to bend. Grain boundaries prevent deformations from flowing through the metal. Therefore, pieces of metal with fewer grain boundaries tend to be ductile, while pieces of metal with more grain boundaries tend to be brittle.
(Note that the actual number of atoms is small compared to a real metal sample and the metal is only two-dimensional. In addition, the movement of the atoms is limited to discrete patch sizes.)
## HOW TO USE IT
Buttons:
SETUP: Resets the simulation, and sets the metal to the correct size.
GO-ONCE: Runs the simulation for one time step.
GO: Runs the simulation continuously until either the GO button is pressed again, or all of the atoms are frozen.
Sliders:
BOX-WIDTH: How many atoms wide the metal is.
FILL-PERCENTAGE: What percentage of the box contains atoms. Smaller values allow for more movement.
ROOM-TEMP: Varies the temperature of the room.
INIT-METAL-TEMP: Varies the initial temperature of the metal.
MELTING-TEMP: Varies the temperature at which the metal solidifies.
Monitors:
AVE-METAL-TEMP: Monitors the average temperature of all the atoms.
Switches:
HISTOGRAM?: Turns the histogram plotting on and off. Turning off the histogram speeds up the model.
Graphs:
AVERAGE METAL TEMPERATURE: Plots the average temperature of all the metal over time.
NUMBER SOLIDIFIED: Plots how many metal atoms are below the melting temperature over time.
TEMPERATURES: Histograms how many atoms are in each temperature range. (Note that the colors of the histogram match the actual colors of the atoms.)
## THINGS TO TRY
Set BOX-WIDTH to 15, FILL-PERCENTAGE to 85, and leave the rest of the sliders at their initial values (ROOM-TEMP at 20, INIT-METAL-TEMP at 1550, and MELTING-TEMP at 500). Run the entire simulation by clicking on SETUP and GO, and then waiting for the metal to completely crystallize. Repeat this several times. What happens to the empty spaces between the atoms? How do you think this would affect the properties of the overall metal?
Now set BOX-WIDTH to 29 and leave the rest of the settings how they were in the previous paragraph. As before, run the entire simulation by clicking on SETUP and GO, and then waiting for the metal to completely crystallize. What are some things that are different this time? What stayed the same?
Set ROOM-TEMP to -20, INIT-METAL-TEMP to 1550, and MELTING-TEMP to 1500. Leave BOX-WIDTH at 29 and FILL-PERCENTAGE at 85. Now run the entire simulation. What happens to the empty spaces between the atoms? Why is this different from the previous simulations? How do you think this would affect the properties of the overall metal?
## EXTENDING THE MODEL
This model prevents more than one atom from occupying the same space. However, in three dimensions, atoms are able to move over one another. Change the code so turtles can move to any space inside the boundaries. What does the resulting crystal look like? Can you imagine what this would look like in three dimensions?
Some metal applications require that the metal's grains form long strips across the metal. To achieve this, only one side of the metal is cooled. This causes all of the crystals to begin on one side of the metal, and consequently grow across its length. This is called directional solidification. In the Procedures window, change the code so one side of the room is much cooler than the rest.
## NETLOGO FEATURES
In NetLogo, a turtle's heading specifies which direction the turtle's shape appears. However, in this model, turtles must move in a direction unrelated to their shape direction. To circumvent this, SETXY was used to move the turtles instead of FD.
Note how we can draw a multi-colored histogram. The HISTOGRAM primitive can only draw in one color at a time, but we work around this by calling it over and over again, plotting only one bar each time, and changing the pen color each time.
With every time step, each atom's temperature changes to the average of everything around it. To do this, each turtle has an agent set of all of its neighboring turtles that is updated each time the turtles move. In addition, each turtle has an agent set of all the patches surrounding it that is also updated. Any white patches in the set are on the outside wall. Therefore, the new temperature is taken as the average of the temperatures of the neighbor list, plus the room temperature multiplied by the number of white patches in the set. Therefore, turtles on the edge of the metal will average in the room temperature to their temperature, but other turtles will not.
## RELATED MODELS
Crystallization Basic
Crystallization Directed
## CREDITS AND REFERENCES
Original implementation: Carrie Hobbs, for the Center for Connected Learning and Computer-Based Modeling.
## HOW TO CITE
If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:
* Wilensky, U. (2002). NetLogo Crystallization Moving model. http://ccl.northwestern.edu/netlogo/models/CrystallizationMoving. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
## COPYRIGHT AND LICENSE
Copyright 2002 Uri Wilensky.
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.
This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.
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