# MaterialSim Grain Growth

Model was written in NetLogo 5.0.4
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;; 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.

There are 15 versions of this model.

## Attached files

File | Type | Description | Last updated | |
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MaterialSim Grain Growth.png | preview | preview | about 11 years ago, by Reuven M. Lerner | Download |

MaterialSim Grain Growth.png | preview | Preview for 'MaterialSim Grain Growth' | about 11 years ago, by Uri Wilensky | Download |

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