MaterialSim Grain Growth

;; two different materials or phases
breed [ element1s element1 ]  ;; element1 is the main material
breed [ element2s element1 ]  ;; element2 is the materials which is
                              ;; dispersed inside element1 (second-phase particles)

element1s-own [
  neighbors-6   ;; agentset of 6 neighboring cells
]

turtles-own [
  neighboring-turtles  ;; agentset of surrounding atoms
  sides-exposed        ;; number of sides exposed to walls  (between 0 and 4)
]

globals [
  logtime                          ;; log of time
  colors                           ;; used both to color turtles, and for histogram
  xmax                             ;; max x size
  ymax                             ;; max y size
  average-grain-size               ;; average grain size
  logaverage-grain-size            ;; log of average grain size (for plotting)
  initial-loggrain-size            ;; For grain growth exponent calculation and graphing
  initial-logtime                  ;; For grain growth exponent calculation and graphing
  grain-growth-exponent            ;; Grain growth exponent
  update-plots?                    ;; boolean for updating plots immediately
]

;; setup checks whether user has chosen "import image" or random in the chooser-widget

to setup
  if starting-point = "Random Arrangement" [
    makes-initial-box-random
  ]
  if starting-point = "Import Image" [
    import-image
  ]
  reset-ticks
end 

to setup-hex-grid
  ;; setup the hexagonal grid in which atoms will be placed
  ;; and creates turtles
  set-default-shape element2s "square 2"
  
  ask patches [
    sprout 1 [
      ;; if there is a second element, create the corresponding atoms
      ifelse (percent-element2 > random 100) [
        ;; element2 is the fixed second-phase particle
        set breed element2s
        set color white
        set heading 360
      ]
      [
        ;; element1 is the main material which grows grains
        set breed element1s
        set shape atom-shape
        set color random 139
        ;; to ensure that the colors are distinct, we only let
        ;; colors deviate from base color by plus or minus 3
        set color one-of base-colors - 3 + random 6
        set heading color
      ]      
      ;; shift even columns down
      if pxcor mod 2 = 0  [ set ycor ycor - 0.5 ] 
    ] 
  ]
  
  ; the two lines below are for NetLogo 3D. Uncomment them, if you are using NetLogo 3D.
  ; ask element1s [ set shape3d "sphere" ]
  ; ask element2s [ set shape3d "cube" ]
  
  ;; now set up the neighbors6 agentsets
  ask element1s [
    ;; define neighborhood of atoms
    ifelse pxcor mod 2 = 0
      [ set neighbors-6 element1s-on patches at-points [[0 1] [1 0] [1 -1] [0 -1] [-1 -1] [-1 0]] ]
      [ set neighbors-6 element1s-on patches at-points [[0 1] [1 1] [1  0] [0 -1] [-1  0] [-1 1]] ] 
  ]
end 

;; makes initial box for image import

to makes-initial-box
  setup-hex-grid
end 

;; makes initial box for random arrangement

to makes-initial-box-random
  clear-all
  setup-hex-grid
end 

;; import image into turtles

to import-image
  clear-all
  let file user-file
  if file = false [ stop ]
  ;; imports image into patches
  import-pcolors file
  ;; converts the square grid to an hex grid
  makes-initial-box
  
  ;; transfers the image to the turtles. Rounds the color values to be integers.
  ask turtles [
    set color round pcolor
    set heading color
  ]
  
  ;; erases the patches (sets their color back to black),
  ask patches [ set pcolor black ]
  reset-ticks
end 

to define-neighboring-turtles
  ;; defines neighboring turtles. Some are "off" because atoms are in hexagons
  ask turtles [
    set neighboring-turtles (turtles at-points [
      [-1  1] [ 0  1] [1  1]
      [-1  0] [ 0  0] [1  0]
      [-1 -1] [ 0 -1] [1 -1]
    ])
  ]  
end 

to go  
  ;;initiates grain growth
  let total-atoms count turtles
  
  ;; stops when there is just one grain
  if average-grain-size >= total-atoms [ stop ]
  
  ;;limits grain growth to element1, element2 represent the stationary second-phase particles
  ask element1s [grain-growth]
  
;  ;; calculates grain variables at a given frequency to save CPU processing
;  ;; we + 1 to ticks to put it in sync with plots (that are updated in 'tick')
;  if remainder (ticks + 1) ticks-per-measurement = 0 [
;    count-grains-and-measure-grain-size
;  ]
  
  ;; advance Monte Carlo Steps (simulation time)
  ;; one Monte Carlo Step represents 'n' reorientation attemps,
  ;; where 'n' is the total number of atoms
  tick 
end 

to count-grains-and-measure-grain-size
  ;; we only do this for ticks > 0 since we can't take log of 0
  if ticks > 0 [
    set logtime log ticks 10
  ]
  grain-count
  if average-grain-size != 0 [
    set logaverage-grain-size (log (average-grain-size) 10)
  ]
  ;; we set the initial log time and grain size at 20 (we don't start
  ;; calculating grain size until then to give the system a bit of time to stabilize
  if ticks = 20 [
    set initial-logtime logtime
    set initial-loggrain-size logaverage-grain-size
  ]
  ;; only initiates grain size calculation after 20 ticks
  if ticks > 20 [
    ;; calculate the angular coefficient of the grain growth curve
    ;; since it is a log-log plot, it's the grain growth exponent
    set grain-growth-exponent (-1 * ((logaverage-grain-size - initial-loggrain-size) /
      (initial-logtime - logtime)))
  ]
end 

to grain-count
  ;; count number of grains based on the number of linear intercepts
  
  let orientation-for-intercept-count 90 ;; direction of intercepts count
  let intercepts 0
  let total-atoms count turtles
  
  ;; asking only elements1 with xcor less than 24
  ;; those at 24 are on the 'edge of the world' which means
  ;; that they will never have neighbors to their right.
  ;; we therefore simply ignore them for this purpose.
  ask element1s with [ xcor < 24 ] [
    ;; checks if there is a turtle to the right for the intercept calculation
    let target-patch patch-at-heading-and-distance orientation-for-intercept-count 1
    ifelse target-patch != nobody and any? turtles-on target-patch [
      ;; If there is a turtle, checks if the heading is different.
      let right-neighbor one-of turtles-on target-patch
      if heading != [ heading ] of right-neighbor [
        ;; If heading is different, add 1 to 'intercepts'.
        set intercepts (intercepts + 1)
      ]
    ]
    [
      ;; if there is no turtle, simply add 1 to 'intercepts'.
      ;; A turtle/nothing interface is considered as grain boundary.
      set intercepts (intercepts + 1)
    ]
  ]
  ;; we add one to intercepts so that zero intercepts = one grain, one intercept = 2 grains, etc.
  set average-grain-size total-atoms / (intercepts + 1)
end 


;; Grain growth procedure - free energy minimization
;; if another random crystallographic heading minimizes energy, switches headings, otherwise keeps the same.

to grain-growth
  ;; if atom has no neighbors, it is surrounded by element2s, and will not change its orientation
  if not any? neighbors-6 [ stop ]
  
  ;; calculates the PRESENT free energy
  let present-heading (heading)
  let present-free-energy count neighbors-6 with [ heading != present-heading ]
  
  ;; chooses a random orientation
  let future-heading ([heading] of (one-of neighbors-6))
  
  ;; calculates the FUTURE free energy, with the random orientation just chosen
  let future-free-energy count neighbors-6 with [ heading != future-heading ]
  
  ;; compares PRESENT and FUTURE free-energies; the lower value "wins"
  ifelse future-free-energy <= present-free-energy
    [ set heading future-heading ]
    [ if (annealing-temperature > random-float 100) [ set heading (future-heading) ] ]
  ;; this last line simulates thermal agitation (adds more randomness to the simulation)
  
  ;;update the color of the atoms
  set color heading
end 

;; drawing procedure

to turtle-draw
  if mouse-down? [    ;; reports true or false to indicate whether mouse button is down
    ask patch mouse-xcor mouse-ycor [
      ask element1s in-radius brush-size [
        set color read-from-string draw-color
        set heading color
      ]
    ]
    display
  ]
end 

;; in the drawing mode, erases the whole "canvas" with red

to erase-all
  ask element1s [
    set color red 
    set heading color
  ]
end 


; Copyright 2005 Uri Wilensky.
; See Info tab for full copyright and license.