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Author Topic: Sodium Chloride  (Read 10917 times)

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Offline SMcNeill

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Re: Sodium Chloride
« Reply #15 on: November 14, 2018, 02:17:09 pm »
I see you dedicated your work here to Pete:

Code: QB64: [Select]
  1. CONST NoBalls%%

;D
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Offline Pete

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Re: Sodium Chloride
« Reply #16 on: November 14, 2018, 02:33:01 pm »
Maybe so, but at least I have a giant dick following me around. How big? Well if I had to estimate the size, I'd say it could cover a large piece of farmland in Virginia! Is this about the battery thingy? If so, don't blame me. I didn't tell you to buy the energizer brand. They just keep going and going...

Pete :D
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Offline STxAxTIC

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Re: Sodium Chloride
« Reply #17 on: November 14, 2018, 06:27:06 pm »
Hey this reminds me, what happens when you install the batteries backwards in the energizer bunny? Not going and going anymore, but...
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Offline Pete

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Re: Sodium Chloride
« Reply #18 on: November 14, 2018, 07:55:37 pm »
How do you keep coming up with these? Or... Would you like some assault with your batteries? Just ask Michael Avenatti!

I thought this was an interesting read regarding crystallization: https://phys.org/news/2013-02-theory-crystal-formation.html

@BPlus By the way, not all salt crystals are cubic in nature, although that is said to be the most energetic stable formation...

"Not all salt appears cubic. Try some different brands. Check out Maldon, which has a hollow pyramid shape. Rock Salt is,, well,, rocky shaped. And Cornish Sea Salt almost resembles hailstones."

So I think Qwerkey just needs to rename his project to Cornish Sea Salt Formation. Either that, or stick some batteries backwards in an Energizer bunny.... and run!

Pete

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Offline Qwerkey

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Re: Sodium Chloride
« Reply #19 on: November 15, 2018, 04:40:12 am »
Quote from: Ashish on November 14, 2018, 09:23:44 am
Hi! I see (in simulation) some NaCl atom which also make bond with another Na or Cl atom. Is this correct?
As, the NaCl is already stable.
Ashish, you are very perceptive.  This program assumes that sodium and chlorine ions are randomly distributed at prgoram start - yet they would not be ions until a bond is formed.  So, yes, the model is not a good simulation of actual chemistry.  But I had thought that NaCl crystals can form from a water solution where the ions are effectively almost free.  And Pete points us to how complicated that can be.  Interesting, isn't it?

I may do a version where NaCl pairs are already formed at program start and see what happens in my model.
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Offline Qwerkey

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Re: Sodium Chloride
« Reply #20 on: November 15, 2018, 07:07:47 am »
Here is version 4A.  In this model, NaCl pairs are gradually introduced around the forming crystal.  At first, the forces are only the spherical inverse-square ones of version 1, and so a sphere forms.  When all pairs (125) are in place, the p-orbital orthogonal electronic force is switched on and the crystal forms into a cubic structure.  In some cases, the ions are absent from a lattice place or there can be two ions in one place - I'm introducing lattice defects!  (No, I'm not: it's a rubbish model).  You will find that the build up of the crystal is slow at first and then speeds up.
Code: QB64: [Select]
  1. 'Simple Model of Ionic Crystal v4A by QWERKEY 2018-11-15
  2. '!!! Can get two atoms sitting on the same place - TBF
  3.  
  4. CONST True = -1`, False = 0`
  5. CONST A0! = 100, A1! = 2, R0! = 250, R1! = 2.3, A2! = 200, R2! = 115, FMin! = -5 '-55
  6. CONST TotBalls%% = 125, Atom! = 110, Kelvin! = 0.35, F1! = 1000, F2! = 3000, Xstal! = 0.993, Adjacent! = 0.2
  7. CONST BallSize1%% = 25, BallSize0%% = 30, Offset% = 730, ScreenX% = 1260, ScreenY% = 800
  8.  
  9. DIM SHARED SodiumPos!(TotBalls%% - 1, 2), ChlorinePos!(TotBalls%% - 1, 2) 'Sodium 1, Chlorine 0
  10. DIM SHARED SodiumVel!(TotBalls%% - 1, 2), ChlorineVel!(TotBalls%% - 1, 2), Theta! '= 0.0084
  11. DIM SodiumAcc!(TotBalls%% - 1, 2), ChlorineAcc!(TotBalls%% - 1, 2), BallStats%(1, 2)
  12.  
  13. _TITLE "Very Accurate Quantum Physics Model"
  15.  
  16. FOR N%% = 0 TO TotBalls%% - 1
  17.     FOR M%% = 0 TO 2
  18.         IF N%% = 0 THEN
  19.             ChlorinePos!(N%%, M%%) = Atom! * (RND - 0.5)
  20.         ELSE
  21.             ChlorinePos!(N%%, M%%) = Atom! * (1 + (RND * (1 + (N%% / TotBalls%%))))
  22.             IF RND > 0.5 THEN ChlorinePos!(N%%, M%%) = -ChlorinePos!(N%%, M%%)
  23.         END IF
  24.         ChlorineVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  25.         SodiumVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  26.     NEXT M%%
  27. NEXT N%%
  28. FOR N%% = 0 TO TotBalls%% - 1
  29.     Phi! = 2 * _PI * RND
  30.     Psi! = _PI * RND ' theta
  31.     SodiumPos!(N%%, 2) = ChlorinePos!(N%%, 2) + Atom! * SIN(Psi!) * COS(Phi!)
  32.     SodiumPos!(N%%, 0) = ChlorinePos!(N%%, 0) + Atom! * SIN(Psi!) * SIN(Phi!)
  33.     SodiumPos!(N%%, 1) = ChlorinePos!(N%%, 1) + Atom! * COS(Psi!)
  34. NEXT N%%
  35.  
  36. ' Ball Colours (Cyperium Method)
  37. DATA 0,0,255
  38. DATA 255,0,0
  39. FOR N%% = 0 TO 1
  40.     FOR P%% = 0 TO 2
  41.         READ BallStats%(N%%, P%%)
  42.     NEXT P%%
  43.     TempImage& = _NEWIMAGE(256, 256, 32)
  44.     _DEST TempImage&
  45.     COLOR _RGBA(BallStats%(N%%, 0), BallStats%(N%%, 1), BallStats%(N%%, 2), 65), _RGBA(0, 0, 0, 0)
  46.     'Image data goes from 1 to 255 (not 0 to 255)
  47.     FOR Z% = 128 TO 255
  48.         FOR X% = 1 TO 255
  49.             FOR Y% = 1 TO 255
  50.                 DeltaX% = X% - 127
  51.                 DeltaY% = Y% - 127
  52.                 DeltaZ% = Z% - 127
  53.                 Dist! = SQR((DeltaX% * DeltaX%) + (DeltaY% * DeltaY%) + (DeltaZ% * DeltaZ%))
  54.                 IF Dist! > 125 AND Dist! < 127 THEN PSET (X%, Y%), _RGBA(CINT(Z% * BallStats%(N%%, 0) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 1) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 2) * (1 - (XBright! * X% / 255)) / 255), 65)
  55.             NEXT
  56.         NEXT
  57.     NEXT
  58.     IF N%% = 0 THEN
  59.         Chlorine& = _COPYIMAGE(TempImage&, 33)
  60.     ELSE
  61.         Sodium& = _COPYIMAGE(TempImage&, 33)
  62.     END IF
  63.     _FREEIMAGE TempImage&
  64. NEXT N%%
  65.  
  66. TempImage& = _NEWIMAGE(102, 2, 32)
  67. _DEST TempImage&
  68. LINE (0, 0)-(101, 1), _RGB32(255, 255, 255), BF
  69. LineImage& = _COPYIMAGE(TempImage&, 33)
  70. _FREEIMAGE TempImage&
  71.  
  72. 'Create screen
  73. SCREEN _NEWIMAGE(ScreenX%, ScreenY%, 32)
  76. _DISPLAYORDER _HARDWARE , _SOFTWARE 'do not even render the software layer, just the hardware one.
  77.  
  78. NoBalls%% = 2
  79. Generate` = False
  80. Count% = 0
  82.     _LIMIT 25
  83.     CALL CentreOfMass
  84.     MaxDist! = 0
  85.     FOR N%% = 0 TO NoBalls%% - 1
  86.         XTemp! = XDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2))): ZTemp! = ZDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2)))
  87.         _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Chlorine& TO(-(BallSize1%% - 1) \ 2 + XTemp!, (BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((BallSize1%% - 1) \ 2 + XTemp!, (BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(BallSize1%% - 1) \ 2 + XTemp!, -(BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  88.         _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Chlorine& TO((BallSize1%% - 1) \ 2 + XTemp!, -(BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(BallSize1%% - 1) \ 2 + XTemp!, -(BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((BallSize1%% - 1) \ 2 + XTemp!, (BallSize1%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  89.         XTemp! = XDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2))): ZTemp! = ZDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2)))
  90.         _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Sodium& TO(-(BallSize0%% - 1) \ 2 + XTemp!, (BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((BallSize0%% - 1) \ 2 + XTemp!, (BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(BallSize0%% - 1) \ 2 + XTemp!, -(BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  91.         _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Sodium& TO((BallSize0%% - 1) \ 2 + XTemp!, -(BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(BallSize0%% - 1) \ 2 + XTemp!, -(BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((BallSize0%% - 1) \ 2 + XTemp!, (BallSize0%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  92.         FOR M%% = 0 TO 2
  93.             SodiumAcc!(N%%, M%%) = 0
  94.         NEXT M%%
  95.         FOR M%% = 0 TO 2
  96.             ChlorineAcc!(N%%, M%%) = 0
  97.         NEXT M%%
  98.         FOR L%% = 0 TO NoBalls%% - 1
  99.             'opposites
  100.             D! = SQR((SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  101.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  102.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  103.             FOR M%% = 0 TO 2
  104.                 SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  105.             NEXT M%%
  106.             IF D! < Atom! THEN
  107.                 '_MAPTRIANGLE (0, 0)-(101, 0)-(101, 1), LineImage& TO(XDash!(SodiumPos!(N%%, 0), SodiumPos!(N%%, 2)), SodiumPos!(N%%, 1), ZDash!(SodiumPos!(N%%, 0), SodiumPos!(N%%, 2)) - Offset%)-(XDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)), ChlorinePos!(L%%, 1), ZDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)) - Offset%)-(XDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)), ChlorinePos!(L%%, 1), ZDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)) - Offset% - 1), , _SMOOTH
  108.                 IF NoBalls%% = TotBalls%% THEN
  109.                     IF ABS(SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) > ABS(SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) AND ABS(SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) > ABS(SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)) THEN
  110.                         delta! = SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)
  111.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  112.                             SodiumPos!(N%%, 1) = SodiumPos!(N%%, 1) + delta! * (1 - Xstal!)
  113.                             ChlorinePos!(L%%, 1) = ChlorinePos!(L%%, 1) - delta! * (1 - Xstal!)
  114.                         END IF
  115.                         delta! = SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)
  116.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  117.                             SodiumPos!(N%%, 2) = SodiumPos!(N%%, 2) + delta! * (1 - Xstal!)
  118.                             ChlorinePos!(L%%, 2) = ChlorinePos!(L%%, 2) - delta! * (1 - Xstal!)
  119.                         END IF
  120.                     ELSEIF ABS(SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) > ABS(SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) AND ABS(SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) > ABS(SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)) THEN
  121.                         delta! = SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)
  122.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  123.                             SodiumPos!(N%%, 0) = SodiumPos!(N%%, 0) + delta! * (1 - Xstal!)
  124.                             ChlorinePos!(L%%, 0) = ChlorinePos!(L%%, 0) - delta! * (1 - Xstal!)
  125.                         END IF
  126.                         delta! = SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)
  127.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  128.                             SodiumPos!(N%%, 2) = SodiumPos!(N%%, 2) + delta! * (1 - Xstal!)
  129.                             ChlorinePos!(L%%, 2) = ChlorinePos!(L%%, 2) - delta! * (1 - Xstal!)
  130.                         END IF
  131.                     ELSE
  132.                         delta! = SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)
  133.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  134.                             SodiumPos!(N%%, 1) = SodiumPos!(N%%, 1) + delta! * (1 - Xstal!)
  135.                             ChlorinePos!(L%%, 1) = ChlorinePos!(L%%, 1) - delta! * (1 - Xstal!)
  136.                         END IF
  137.                         delta! = SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)
  138.                         IF ABS(delta!) > Adjacent! * Atom! THEN
  139.                             SodiumPos!(N%%, 0) = SodiumPos!(N%%, 0) + delta! * (1 - Xstal!)
  140.                             ChlorinePos!(L%%, 0) = ChlorinePos!(L%%, 0) - delta! * (1 - Xstal!)
  141.                         END IF
  142.                     END IF
  143.                 END IF
  144.                 IF N%% = NoBalls%% - 1 AND L%% < N%% AND NOT Generate` THEN
  145.                     Generate` = True
  146.                 END IF
  147.             END IF
  148.             D! = SQR((SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) * (SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) + (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) * (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) + (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)) * (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)))
  149.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  150.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  151.             FOR M%% = 0 TO 2
  152.                 ChlorineAcc!(N%%, M%%) = F! * (SodiumPos!(L%%, M%%) - ChlorinePos!(N%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  153.             NEXT M%%
  154.             IF D! < Atom! THEN
  155.                 IF N%% = NoBalls%% - 1 AND L%% < N%% AND NOT Generate` THEN
  156.                     Generate` = True
  157.                 END IF
  158.             END IF
  159.             IF L%% <> N%% THEN
  160.                 'same type
  161.                 D! = SQR((SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) * (SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) + (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) * (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) + (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)) * (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)))
  162.                 F! = -(Attraction!(D!)) / F2!
  163.                 FOR M%% = 0 TO 2
  164.                     SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - SodiumPos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  165.                 NEXT M%%
  166.                 D! = SQR((ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  167.                 F! = -(Attraction!(D!)) / F2!
  168.                 FOR M%% = 0 TO 2
  169.                     ChlorineAcc!(N%%, M%%) = -F! * (ChlorinePos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  170.                 NEXT M%%
  171.             END IF
  172.         NEXT L%%
  173.         FOR M%% = 0 TO 2
  174.             SodiumPos!(N%%, M%%) = SodiumPos!(N%%, M%%) + SodiumVel!(N%%, M%%)
  175.             ChlorinePos!(N%%, M%%) = ChlorinePos!(N%%, M%%) + ChlorineVel!(N%%, M%%)
  176.             SodiumVel!(N%%, M%%) = SodiumVel!(N%%, M%%) + SodiumAcc!(N%%, M%%)
  177.             IF ABS(SodiumVel!(N%%, M%%)) > Kelvin! THEN SodiumVel!(N%%, M%%) = Kelvin! * (ABS(SodiumVel!(N%%, M%%)) / SodiumVel!(N%%, M%%))
  178.             ChlorineVel!(N%%, M%%) = ChlorineVel!(N%%, M%%) + ChlorineAcc!(N%%, M%%)
  179.             IF ABS(ChlorineVel!(N%%, M%%)) > Kelvin! THEN ChlorineVel!(N%%, M%%) = Kelvin! * (ABS(ChlorineVel!(N%%, M%%)) / ChlorineVel!(N%%, M%%))
  180.         NEXT M%%
  181.     NEXT N%%
  182.     Theta! = Theta! + 0.008
  183.     IF Theta! > _PI THEN Theta! = Theta! - 2 * _PI
  184.     Count% = Count% + 1
  185.     IF (Generate` OR Count% = 300) AND NoBalls%% < TotBalls% THEN
  186.         NoBalls%% = NoBalls%% + 1
  187.         Generate` = False        
  188.     END IF
  189.     IF Count% = 300 THEN Count% = 0
  190.     LOCATE 1, 1: PRINT NoBalls%%;
  191.     _DISPLAY
  193.  
  195.  
  196. FUNCTION Attraction! (Dist!)
  197.     Attraction! = A0! * (1 / (Dist! / A2!) ^ A1!)
  199.  
  200. FUNCTION Repulsion! (Dist!)
  201.     Repulsion! = -R0! * (1 / (Dist! / R2!) ^ R1!)
  203.  
  204. FUNCTION XDash! (X!, Z!)
  205.     XDash! = X! * COS(Theta!) + Z! * SIN(Theta!)
  207.  
  208. FUNCTION ZDash! (X!, Z!)
  209.     ZDash! = -X! * SIN(Theta!) + Z! * COS(Theta!)
  211.  
  212. SUB CentreOfMass 'fio centre of mass adjustment & zero net momentums
  213.     TotMass# = 0
  214.     MRx# = 0: MRy# = 0: MRz# = 0
  215.     Px# = 0: Py# = 0: Pz# = 0
  216.     FOR N% = 0 TO TotBalls%% - 1
  217.         TotMass# = TotMass# + 1
  218.         MRx# = MRx# + SodiumPos!(N%, 0)
  219.         MRy# = MRy# + SodiumPos!(N%, 1)
  220.         MRz# = MRz# + SodiumPos!(N%, 2)
  221.         Px# = SodiumVel!(N%, 0) + Px#
  222.         Py# = SodiumVel!(N%, 1) + Py#
  223.         Pz# = SodiumVel!(N%, 2) + Pz#
  224.         TotMass# = TotMass# + 1
  225.         MRx# = MRx# + ChlorinePos!(N%, 0)
  226.         MRy# = MRy# + ChlorinePos!(N%, 1)
  227.         MRz# = MRz# + ChlorinePos!(N%, 2)
  228.         Px# = ChlorineVel!(N%, 0) + Px#
  229.         Py# = ChlorineVel!(N%, 1) + Py#
  230.         Pz# = ChlorineVel!(N%, 2) + Pz#
  231.     NEXT N%
  232.     FOR N% = 0 TO TotBalls%% - 1
  233.         SodiumPos!(N%, 0) = SodiumPos!(N%, 0) - (MRx# / TotMass#)
  234.         SodiumPos!(N%, 1) = SodiumPos!(N%, 1) - (MRy# / TotMass#)
  235.         SodiumPos!(N%, 2) = SodiumPos!(N%, 2) - (MRz# / TotMass#)
  236.         SodiumVel!(N%, 0) = SodiumVel!(N%, 0) - (Px# / TotMass#)
  237.         SodiumVel!(N%, 1) = SodiumVel!(N%, 1) - (Py# / TotMass#)
  238.         SodiumVel!(N%, 2) = SodiumVel!(N%, 2) - (Pz# / TotMass#)
  239.         ChlorinePos!(N%, 0) = ChlorinePos!(N%, 0) - (MRx# / TotMass#)
  240.         ChlorinePos!(N%, 1) = ChlorinePos!(N%, 1) - (MRy# / TotMass#)
  241.         ChlorinePos!(N%, 2) = ChlorinePos!(N%, 2) - (MRz# / TotMass#)
  242.         ChlorineVel!(N%, 0) = ChlorineVel!(N%, 0) - (Px# / TotMass#)
  243.         ChlorineVel!(N%, 1) = ChlorineVel!(N%, 1) - (Py# / TotMass#)
  244.         ChlorineVel!(N%, 2) = ChlorineVel!(N%, 2) - (Pz# / TotMass#)
  245.     NEXT N%
  247.  
« Last Edit: November 18, 2018, 07:22:40 am by Qwerkey »
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Offline Qwerkey

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Re: Sodium Chloride
« Reply #21 on: November 18, 2018, 05:04:32 am »
Here is version 5.  In this probably final version, Na Cl pairs are gradually introduced.  The forces are adjusted so that there is a preferential attraction at each sodium ion for chlorines at the six orthogonal positions.  In the model, these directions are aligned with the grid x-, y-, and z- axes (even though there is viewing rotation around the y- axis).  In reality, of course, there is no such directional preference, but I could not fathom the mathematics for 3-dimensional individual atom axes rotations.

The model does lead to a final arrangement into some sort of cubic structure (you will have to let it run for some time after the final quantity, 125, is reached).  If we had a crystallographer, he or she might be able to say what sort of structure it is or even if the final structure is always the same.
Code: QB64: [Select]
  1. 'Simple Model of Ionic Crystal v5 by QWERKEY 2018-11-18
  2.  
  3. CONST True = -1`, False = 0`
  4. CONST A0! = 100, A1! = 2, R0! = 250, R1! = 2.3, A2! = 200, R2! = 115, FMin! = -5 '-55
  5. CONST TotBalls%% = 125, Atom! = 110, Kelvin! = 0.35, F1! = 1000, F2! = 3000, Xstal! = 0.98
  6. CONST ChlorineSize%% = 35, SodiumSize%% = 25, Offset% = 730, ScreenX% = 1260, ScreenY% = 800, ThetaMax! = 0.5
  7.  
  8. DIM SHARED SodiumPos!(TotBalls%% - 1, 2), ChlorinePos!(TotBalls%% - 1, 2), NoBalls%%
  9. DIM SHARED SodiumVel!(TotBalls%% - 1, 2), ChlorineVel!(TotBalls%% - 1, 2), ViewAngle!
  10. DIM SodiumAcc!(TotBalls%% - 1, 2), ChlorineAcc!(TotBalls%% - 1, 2), BallStats%(1, 2)
  11.  
  12. _TITLE "Very Accurate Quantum Physics Model"
  14.  
  15. FOR N%% = 0 TO TotBalls%% - 1
  16.     FOR M%% = 0 TO 2
  17.         IF N%% = 0 THEN
  18.             ChlorinePos!(N%%, M%%) = Atom! * (RND - 0.5)
  19.         ELSE
  20.             ChlorinePos!(N%%, M%%) = Atom! * (1 + (RND * (1 + (N%% / TotBalls%%))))
  21.             IF RND > 0.5 THEN ChlorinePos!(N%%, M%%) = -ChlorinePos!(N%%, M%%)
  22.         END IF
  23.         ChlorineVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  24.         SodiumVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  25.     NEXT M%%
  26.     Chi! = 2 * _PI * RND
  27.     Psi! = _PI * RND
  28.     SodiumPos!(N%%, 2) = ChlorinePos!(N%%, 2) + Atom! * SIN(Psi!) * COS(Chi!)
  29.     SodiumPos!(N%%, 0) = ChlorinePos!(N%%, 0) + Atom! * SIN(Psi!) * SIN(Chi!)
  30.     SodiumPos!(N%%, 1) = ChlorinePos!(N%%, 1) + Atom! * COS(Psi!)
  31. NEXT N%%
  32.  
  33. ' Ball Colours (Cyperium Method)
  34. DATA 0,0,255
  35. DATA 255,0,0
  36. FOR N%% = 0 TO 1
  37.     FOR P%% = 0 TO 2
  38.         READ BallStats%(N%%, P%%)
  39.     NEXT P%%
  40.     TempImage& = _NEWIMAGE(256, 256, 32)
  41.     _DEST TempImage&
  42.     COLOR _RGBA(BallStats%(N%%, 0), BallStats%(N%%, 1), BallStats%(N%%, 2), 65), _RGBA(0, 0, 0, 0)
  43.     'Image data goes from 1 to 255 (not 0 to 255)
  44.     FOR Z% = 128 TO 255
  45.         FOR X% = 1 TO 255
  46.             FOR Y% = 1 TO 255
  47.                 DeltaX% = X% - 127
  48.                 DeltaY% = Y% - 127
  49.                 DeltaZ% = Z% - 127
  50.                 Dist! = SQR((DeltaX% * DeltaX%) + (DeltaY% * DeltaY%) + (DeltaZ% * DeltaZ%))
  51.                 IF Dist! > 125 AND Dist! < 127 THEN PSET (X%, Y%), _RGBA(CINT(Z% * BallStats%(N%%, 0) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 1) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 2) * (1 - (XBright! * X% / 255)) / 255), 65)
  52.             NEXT
  53.         NEXT
  54.     NEXT
  55.     IF N%% = 0 THEN
  56.         Sodium& = _COPYIMAGE(TempImage&, 33)
  57.     ELSE
  58.         Chlorine& = _COPYIMAGE(TempImage&, 33)
  59.     END IF
  60.     _FREEIMAGE TempImage&
  61. NEXT N%%
  62.  
  63. TempImage& = _NEWIMAGE(102, 2, 32)
  64. _DEST TempImage&
  65. LINE (0, 0)-(101, 1), _RGB32(255, 255, 255), BF
  66. LineImage& = _COPYIMAGE(TempImage&, 33)
  67. _FREEIMAGE TempImage&
  68.  
  69. 'Create screen
  70. SCREEN _NEWIMAGE(ScreenX%, ScreenY%, 32)
  73. _DISPLAYORDER _HARDWARE , _SOFTWARE 'do not even render the software layer, just the hardware one.
  74.  
  75. NoBalls%% = 2
  76. Generate` = False
  77. Count% = 0
  79.     _LIMIT 25
  80.     '_LIMIT 5
  81.     CALL CentreOfMass
  82.     MaxDist! = 0
  83.     FOR N%% = 0 TO NoBalls%% - 1
  84.         XTemp! = XDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2))): ZTemp! = ZDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2)))
  85.         _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Chlorine& TO(-(ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  86.         _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Chlorine& TO((ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  87.         XTemp! = XDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2))): ZTemp! = ZDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2)))
  88.         _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Sodium& TO(-(SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  89.         _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Sodium& TO((SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  90.         FOR M%% = 0 TO 2
  91.             SodiumAcc!(N%%, M%%) = 0
  92.         NEXT M%%
  93.         FOR M%% = 0 TO 2
  94.             ChlorineAcc!(N%%, M%%) = 0
  95.         NEXT M%%
  96.         FOR L%% = 0 TO NoBalls%% - 1
  97.             'opposites
  98.             D! = SQR((SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  99.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  100.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  101.             FOR M%% = 0 TO 2
  102.                 SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  103.             NEXT M%%
  104.             IF D! < Atom! THEN
  105.                 IF N%% = NoBalls%% - 1 AND L%% < N%% AND NOT Generate` THEN
  106.                     Generate` = True
  107.                 END IF
  108.             END IF
  109.             D! = SQR((SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) * (SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) + (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) * (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) + (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)) * (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)))
  110.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  111.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  112.             FOR M%% = 0 TO 2
  113.                 ChlorineAcc!(N%%, M%%) = F! * (SodiumPos!(L%%, M%%) - ChlorinePos!(N%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  114.             NEXT M%%
  115.             '!!! Might change the generation routine, as well
  116.             IF D! < Atom! THEN
  117.                 IF N%% = NoBalls%% - 1 AND L%% < N%% AND NOT Generate` THEN
  118.                     Generate` = True
  119.                 END IF
  120.             END IF
  121.             IF L%% <> N%% THEN
  122.                 'same type
  123.                 D! = SQR((SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) * (SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) + (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) * (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) + (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)) * (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)))
  124.                 F! = -(Attraction!(D!)) / F2!
  125.                 FOR M%% = 0 TO 2
  126.                     SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - SodiumPos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  127.                 NEXT M%%
  128.                 D! = SQR((ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  129.                 F! = -(Attraction!(D!)) / F2!
  130.                 FOR M%% = 0 TO 2
  131.                     ChlorineAcc!(N%%, M%%) = -F! * (ChlorinePos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  132.                 NEXT M%%
  133.             END IF
  134.         NEXT L%%
  135.         FOR M%% = 0 TO 2
  136.             SodiumPos!(N%%, M%%) = SodiumPos!(N%%, M%%) + SodiumVel!(N%%, M%%)
  137.             ChlorinePos!(N%%, M%%) = ChlorinePos!(N%%, M%%) + ChlorineVel!(N%%, M%%)
  138.             SodiumVel!(N%%, M%%) = SodiumVel!(N%%, M%%) + SodiumAcc!(N%%, M%%)
  139.             IF ABS(SodiumVel!(N%%, M%%)) > Kelvin! THEN SodiumVel!(N%%, M%%) = Kelvin! * (ABS(SodiumVel!(N%%, M%%)) / SodiumVel!(N%%, M%%))
  140.             ChlorineVel!(N%%, M%%) = ChlorineVel!(N%%, M%%) + ChlorineAcc!(N%%, M%%)
  141.             IF ABS(ChlorineVel!(N%%, M%%)) > Kelvin! THEN ChlorineVel!(N%%, M%%) = Kelvin! * (ABS(ChlorineVel!(N%%, M%%)) / ChlorineVel!(N%%, M%%))
  142.         NEXT M%%
  143.     NEXT N%%
  144.     FOR N%% = 0 TO NoBalls%% - 1
  145.         FOR M%% = 0 TO 5 'the six orthogonal positions from each sodium atom
  146.             CALL Orthogonal(N%%, M%%) 'Move chlorine atom
  147.         NEXT M%%
  148.     NEXT N%%
  149.     ViewAngle! = ViewAngle! + 0.008
  150.     IF ViewAngle! > _PI THEN ViewAngle! = ViewAngle! - 2 * _PI
  151.     Count% = Count% + 1
  152.     IF (Generate` OR Count% = 300) AND NoBalls%% < TotBalls% THEN
  153.         'IF Generate` AND NoBalls%% < TotBalls% THEN
  154.         NoBalls%% = NoBalls%% + 1
  155.         Generate` = False
  156.     END IF
  157.     IF Count% = 300 THEN Count% = 0
  158.     LOCATE 1, 1: PRINT NoBalls%%;
  159.     _DISPLAY
  161.  
  163.  
  164. FUNCTION Attraction! (Dist!)
  165.     Attraction! = A0! * (1 / (Dist! / A2!) ^ A1!)
  167.  
  168. FUNCTION Repulsion! (Dist!)
  169.     Repulsion! = -R0! * (1 / (Dist! / R2!) ^ R1!)
  171.  
  172. FUNCTION XDash! (X!, Z!)
  173.     XDash! = X! * COS(ViewAngle!) + Z! * SIN(ViewAngle!)
  175.  
  176. FUNCTION ZDash! (X!, Z!)
  177.     ZDash! = -X! * SIN(ViewAngle!) + Z! * COS(ViewAngle!)
  179.  
  180. SUB Orthogonal (P%%, Q%%)
  181.     OnlyOneChlorine%% = True
  182.     NoChlorines%% = 0
  183.     R%% = 0
  184.     WHILE R%% <= NoBalls%% - 1 AND OnlyOneChlorine%%
  185.         IF R%% <> P%% THEN
  186.             Sepn! = SQR((SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)) * (SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)) + (SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)) * (SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)) + (SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)) * (SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)))
  187.             IF Sepn! < Atom! THEN
  188.                 X! = SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)
  189.                 Y! = SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)
  190.                 Z! = SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)
  191.                 SELECT CASE Q%%
  192.                     CASE 0
  193.                         S1! = SQR(Y! * Y! + Z! * Z!)
  194.                         Theta! = _ATAN2(S1!, X!)
  195.                         IF X! > 0 AND X! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  196.                     CASE 1
  197.                         S1! = SQR(X! * X! + Z! * Z!)
  198.                         Theta! = _ATAN2(S1!, Y!)
  199.                         IF Y! > 0 AND Y! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  200.                     CASE 2
  201.                         S1! = SQR(Y! * Y! + X! * X!)
  202.                         Theta! = _ATAN2(S1!, Z!)
  203.                         IF Z! > 0 AND Z! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  204.                     CASE 3
  205.                         S1! = SQR(Y! * Y! + Z! * Z!)
  206.                         Theta! = _ATAN2(S1!, -X!)
  207.                         IF X! < 0 AND X! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  208.                     CASE 4
  209.                         S1! = SQR(X! * X! + Z! * Z!)
  210.                         Theta! = _ATAN2(S1!, -Y!)
  211.                         IF Y! < 0 AND Y! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  212.                     CASE ELSE '5
  213.                         S1! = SQR(Y! * Y! + X! * X!)
  214.                         Theta! = _ATAN2(S1!, -Z!)
  215.                         IF Z! < 0 AND Z! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  216.                 END SELECT
  217.             END IF
  218.         END IF
  219.         IF OnlyOneChlorine%% THEN
  220.             Sepn! = SQR((ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)) * (ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)) + (ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)) * (ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)) + (ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)) * (ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)))
  221.             IF Sepn! < Atom! THEN
  222.                 X! = ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)
  223.                 Y! = ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)
  224.                 Z! = ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)
  225.                 SELECT CASE Q%%
  226.                     CASE 0
  227.                         S1! = SQR(Y! * Y! + Z! * Z!)
  228.                         Theta! = _ATAN2(S1!, X!)
  229.                         IF X! > 0 AND X! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  230.                             NoChlorines%% = NoChlorines%% + 1
  231.                             ROne%% = R%%
  232.                         END IF
  233.                     CASE 1
  234.                         S1! = SQR(X! * X! + Z! * Z!)
  235.                         Theta! = _ATAN2(S1!, Y!)
  236.                         IF Y! > 0 AND Y! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  237.                             NoChlorines%% = NoChlorines%% + 1
  238.                             ROne%% = R%%
  239.                         END IF
  240.                     CASE 2
  241.                         S1! = SQR(Y! * Y! + X! * X!)
  242.                         Theta! = _ATAN2(S1!, Z!)
  243.                         IF Z! > 0 AND Z! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  244.                             NoChlorines%% = NoChlorines%% + 1
  245.                             ROne%% = R%%
  246.                         END IF
  247.                     CASE 3
  248.                         S1! = SQR(Y! * Y! + Z! * Z!)
  249.                         Theta! = _ATAN2(S1!, -X!)
  250.                         IF X! < 0 AND X! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  251.                             NoChlorines%% = NoChlorines%% + 1
  252.                             ROne%% = R%%
  253.                         END IF
  254.                     CASE 4
  255.                         S1! = SQR(X! * X! + Z! * Z!)
  256.                         Theta! = _ATAN2(S1!, -Y!)
  257.                         IF Y! < 0 AND Y! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  258.                             NoChlorines%% = NoChlorines%% + 1
  259.                             ROne%% = R%%
  260.                         END IF
  261.                     CASE ELSE '5
  262.                         S1! = SQR(Y! * Y! + X! * X!)
  263.                         Theta! = _ATAN2(S1!, -Z!)
  264.                         IF Z! < 0 AND Z! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  265.                             NoChlorines%% = NoChlorines%% + 1
  266.                             ROne%% = R%%
  267.                         END IF
  268.                 END SELECT
  269.                 IF NoChlorines%% > 1 THEN OnlyOneChlorine%% = False
  270.             END IF
  271.         END IF
  272.         R%% = R%% + 1
  273.     WEND
  274.     IF NoChlorines%% = 0 THEN OnlyOneChlorine%% = False
  275.  
  276.     IF OnlyOneChlorine%% THEN
  277.  
  278.         'LOCATE 2, 1
  279.         'PRINT P%%, Q%%, ROne%%
  280.         ''FOR A%% = 0 TO NoBalls%% - 1
  281.         ''    FOR B%% = 0 TO 2
  282.         ''        PRINT A%%, B%%, SodiumPos!(A%%, B%%), ChlorinePos!(A%%, B%%)
  283.         ''    NEXT B%%
  284.         ''NEXT A%%
  285.         'END
  286.         'R%% = R%% - 1
  287.  
  288.         'Move Chlorine Atom
  289.         X! = ChlorinePos!(ROne%%, 0) - SodiumPos!(P%%, 0)
  290.         Y! = ChlorinePos!(ROne%%, 1) - SodiumPos!(P%%, 1)
  291.         Z! = ChlorinePos!(ROne%%, 2) - SodiumPos!(P%%, 2)
  292.         SELECT CASE Q%%
  293.             CASE 0, 3
  294.                 ChlorinePos!(ROne%%, 1) = ChlorinePos!(ROne%%, 1) - Y! * (1 - Xstal!)
  295.                 ChlorinePos!(ROne%%, 2) = ChlorinePos!(ROne%%, 2) - Z! * (1 - Xstal!)
  296.             CASE 1, 4
  297.                 ChlorinePos!(ROne%%, 0) = ChlorinePos!(ROne%%, 0) - X! * (1 - Xstal!)
  298.                 ChlorinePos!(ROne%%, 2) = ChlorinePos!(ROne%%, 2) - Z! * (1 - Xstal!)
  299.             CASE 2, 5
  300.                 ChlorinePos!(ROne%%, 0) = ChlorinePos!(ROne%%, 0) - X! * (1 - Xstal!)
  301.                 ChlorinePos!(ROne%%, 1) = ChlorinePos!(ROne%%, 1) - Y! * (1 - Xstal!)
  302.         END SELECT
  303.     END IF
  304.  
  306.  
  307. SUB CentreOfMass 'fio centre of mass adjustment & zero net momentums
  308.     TotMass# = 0
  309.     MRx# = 0: MRy# = 0: MRz# = 0
  310.     Px# = 0: Py# = 0: Pz# = 0
  311.     FOR N% = 0 TO TotBalls%% - 1
  312.         TotMass# = TotMass# + 1
  313.         MRx# = MRx# + SodiumPos!(N%, 0)
  314.         MRy# = MRy# + SodiumPos!(N%, 1)
  315.         MRz# = MRz# + SodiumPos!(N%, 2)
  316.         Px# = SodiumVel!(N%, 0) + Px#
  317.         Py# = SodiumVel!(N%, 1) + Py#
  318.         Pz# = SodiumVel!(N%, 2) + Pz#
  319.         TotMass# = TotMass# + 1
  320.         MRx# = MRx# + ChlorinePos!(N%, 0)
  321.         MRy# = MRy# + ChlorinePos!(N%, 1)
  322.         MRz# = MRz# + ChlorinePos!(N%, 2)
  323.         Px# = ChlorineVel!(N%, 0) + Px#
  324.         Py# = ChlorineVel!(N%, 1) + Py#
  325.         Pz# = ChlorineVel!(N%, 2) + Pz#
  326.     NEXT N%
  327.     FOR N% = 0 TO TotBalls%% - 1
  328.         SodiumPos!(N%, 0) = SodiumPos!(N%, 0) - (MRx# / TotMass#)
  329.         SodiumPos!(N%, 1) = SodiumPos!(N%, 1) - (MRy# / TotMass#)
  330.         SodiumPos!(N%, 2) = SodiumPos!(N%, 2) - (MRz# / TotMass#)
  331.         SodiumVel!(N%, 0) = SodiumVel!(N%, 0) - (Px# / TotMass#)
  332.         SodiumVel!(N%, 1) = SodiumVel!(N%, 1) - (Py# / TotMass#)
  333.         SodiumVel!(N%, 2) = SodiumVel!(N%, 2) - (Pz# / TotMass#)
  334.         ChlorinePos!(N%, 0) = ChlorinePos!(N%, 0) - (MRx# / TotMass#)
  335.         ChlorinePos!(N%, 1) = ChlorinePos!(N%, 1) - (MRy# / TotMass#)
  336.         ChlorinePos!(N%, 2) = ChlorinePos!(N%, 2) - (MRz# / TotMass#)
  337.         ChlorineVel!(N%, 0) = ChlorineVel!(N%, 0) - (Px# / TotMass#)
  338.         ChlorineVel!(N%, 1) = ChlorineVel!(N%, 1) - (Py# / TotMass#)
  339.         ChlorineVel!(N%, 2) = ChlorineVel!(N%, 2) - (Pz# / TotMass#)
  340.     NEXT N%
  342.  
« Last Edit: November 18, 2018, 07:23:05 am by Qwerkey »
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Offline STxAxTIC

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Re: Sodium Chloride
« Reply #22 on: November 18, 2018, 07:50:05 am »
Marvelous. I let it run for 45 minutes, starting at about half that time, and the crystal grew nice and naturally. Love it.

Say, this leads us to the next phase, right? Start with a perfect crystal, and the displace one of the atoms real quick. The pattern that spreads will be a classic phonon. (Something tells me Qwerkey already knows this is not a misspelling of phoTon.)

Back when taking physics 700-something, a Russian professor had us derive the quantum theory of phonons for an exam, from memory, as a surprise. He used his red pen once on my last page:

http://www.barnesreport.net/scripturam/solid%20state%20physics/Quantum%20Theory%20of%20Phonons.pdf
« Last Edit: November 18, 2018, 07:51:31 am by STxAxTIC »
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Offline Qwerkey

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Re: Sodium Chloride
« Reply #23 on: November 18, 2018, 10:36:49 am »
Quote from: STxAxTIC on November 18, 2018, 07:50:05 am
This leads us to the next phase, right? Start with a perfect crystal, and the displace one of the atoms real quick. The pattern that spreads will be a classic phonon.

Hmm! So our next post will be entitled "Quantum Modelling of Phonon Propagation in the Sodium Chloride Crystal"?  Ambitious!  It would, any at rate, be interesting to see how long it would take Pete to get his irritatingly incessant politics into that.
« Last Edit: November 18, 2018, 10:41:06 am by Qwerkey »
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Offline SMcNeill

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Re: Sodium Chloride
« Reply #24 on: November 18, 2018, 10:56:26 am »
Quote from: Qwerkey on November 18, 2018, 10:36:49 am
Quote from: STxAxTIC on November 18, 2018, 07:50:05 am
This leads us to the next phase, right? Start with a perfect crystal, and the displace one of the atoms real quick. The pattern that spreads will be a classic phonon.

Hmm! So our next post will be entitled "Quantum Modelling of Phonon Propagation in the Sodium Chloride Crystal"?  Ambitious!  It would, any at rate, be interesting to see how long it would take Pete to get his irritatingly incessant politics into that.

Q-Mop Piscc -- Isn't that what illegal immigrates have to do after a Democrat goes to the restroom?  And get underpaid while doing it to boot!

(Ha!  I beat Pete to it.)  ;D

************************

Got to admit, I'm enjoying these little demos.  I'll be happy to watch you Q-Mop Piscc when you do it.  ;)
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Offline Pete

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Re: Sodium Chloride
« Reply #25 on: November 18, 2018, 11:22:42 am »
Quote from: Qwerkey on November 18, 2018, 10:36:49 am
Quote from: STxAxTIC on November 18, 2018, 07:50:05 am
This leads us to the next phase, right? Start with a perfect crystal, and the displace one of the atoms real quick. The pattern that spreads will be a classic phonon.

Hmm! So our next post will be entitled "Quantum Modelling of Phonon Propagation in the Sodium Chloride Crystal"?  Ambitious!  It would, any at rate, be interesting to see how long it would take Pete to get his irritatingly incessant politics into that.

Faster than the separation of of bromide from sodium. That's a long and complicated process, but eventually it can be achieved. I believe it's called a BR-exit.

As for the next version, might I suggest a time lapse version? In other words allow the use of key presses to speed the simulation up. You did a great job of achieving the more traditional and expected cubic crystalline formation, but it's a bit like watching grass grow. I also miss the effects a previous version that produced interactions with white straight lines between the atoms. Why did you decide to remove those? Also, when new molecules join from off the screen, the effect is perfect, but when they appear on the screen, they start out too large, which makes them look more like they just magically appeared, instead of a far away object coming into visual range. I don't know if you'd want to bother tweaking that or not for any further versions, but kudos for making an original program contribution.

Pete
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Offline Qwerkey

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Re: Sodium Chloride
« Reply #26 on: November 23, 2018, 05:04:45 am »
I said that the previous version would be the last - everyone must be fed up with coloured discs moving about the screen, but STxAxTIC & Pete's ideas/suggestions were worthy of note.  So this is the final final version.

Here the program starts with a number of atoms as a seed crystal and then further molecules (atom pairs) are added from outside.  You have the options to draw the bonds and to pause the process.

The program starts with a seed of NaCl atoms in a face-centred cubic crystal with spacings set at the correct final value.  I therefore expected this to be stable and await the addition of the further atoms.  However, you will see the program immediately breaks up this crystal and reforms the atoms into a different crystal arrangement.  You'd have thought that as I am the program creator, I'd be able to get this right, but I suspect that this demonstrates my poor understanding of crystallography.  It takes about 80 seconds for the crystal to reform.

It then takes about 12 minutes for the additional atoms to arrive and be added to the crystal.  The new atoms are different colours (red & blue for seed atoms, pink & cyan for the new ones).  The colour difference is only to show which are the new ones.  They all behave exactly the same.  Some of the new ones may actually end up deeper in the crystal than the original ones.  This shows that the structure is a little fluid.  In reality, this would hardly ever occur as the quantum bonds are very strong.

Code: QB64: [Select]
  1. 'Simple Model of Ionic Crystal v6 by QWERKEY 2018-11-23
  2.  
  3. CONST True = -1`, False = 0`
  4. CONST A0! = 100, A1! = 2, R0! = 250, R1! = 2.3, A2! = 200, R2! = 115, F2! = 3000, FMin! = -5 '-55
  5. CONST TotBalls%% = 125, NoSeed%% = 75, Atom! = 110, Xstal! = 0.98, Kelvin! = 0.35
  6. CONST ChlorineSize%% = 35, SodiumSize%% = 25, Offset% = 730, ScreenX% = 1260, ScreenY% = 800, ThetaMax! = 0.5
  7.  
  8. DIM SHARED SodiumPos!(TotBalls%% - 1, 2), ChlorinePos!(TotBalls%% - 1, 2), NoBalls%%
  9. DIM SHARED SodiumVel!(TotBalls%% - 1, 2), ChlorineVel!(TotBalls%% - 1, 2), ViewAngle!
  10. DIM SodiumAcc!(TotBalls%% - 1, 2), ChlorineAcc!(TotBalls%% - 1, 2), BallStats%(3, 2)
  11.  
  12. _TITLE "Very Accurate Quantum Physics Model"
  14.  
  15. 'Set Seed Crystal
  16. Default! = 0.69 * Atom!
  17. FOR I%% = -2 TO 2
  18.     FOR J%% = -2 TO 2
  19.         FOR K%% = -1 TO 1
  20.             IF J%% \ 2 <> J%% / 1 THEN
  21.                 ChlorinePos!(N%%, 0) = Default! * I%%
  22.                 ChlorinePos!(N%%, 1) = Default! * J%%
  23.                 ChlorinePos!(N%%, 2) = 2 * Default! * K%%
  24.                 SodiumPos!(N%%, 0) = ChlorinePos!(N%%, 0)
  25.                 SodiumPos!(N%%, 1) = ChlorinePos!(N%%, 1)
  26.                 SodiumPos!(N%%, 2) = ChlorinePos!(N%%, 2) - Default!
  27.             ELSE
  28.                 ChlorinePos!(N%%, 0) = Default! * I%%
  29.                 ChlorinePos!(N%%, 1) = Default! * J%%
  30.                 ChlorinePos!(N%%, 2) = 2 * Default! * K%% - Default!
  31.                 SodiumPos!(N%%, 0) = ChlorinePos!(N%%, 0)
  32.                 SodiumPos!(N%%, 1) = ChlorinePos!(N%%, 1)
  33.                 SodiumPos!(N%%, 2) = ChlorinePos!(N%%, 2) + Default!
  34.             END IF
  35.             N%% = N%% + 1
  36.         NEXT K%%
  37.     NEXT J%%
  38. NEXT I%%
  39. FOR N%% = 0 TO NoSeed%% - 1
  40.     FOR M%% = 0 TO 2
  41.         ChlorineVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  42.         SodiumVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  43.     NEXT M%%
  44. NEXT N%%
  45. 'Additional atom properties
  46. FOR N%% = NoSeed% TO TotBalls%% - 1
  47.     Xi! = RND * _PI / 4 '0.5
  48.     ChlorinePos!(N%%, 0) = (1 + 0.75 * RND) * ScreenX% / 3
  49.     IF RND > 0.5 THEN ChlorinePos!(N%%, 0) = ChlorinePos!(N%%, 0) * -1
  50.     Chi! = 2 * _PI * RND
  51.     RPosn! = ChlorinePos!(N%%, 0) * TAN(Xi!)
  52.     ChlorinePos!(N%%, 1) = RPosn! * SIN(Chi!)
  53.     ChlorinePos!(N%%, 2) = RPosn! * COS(Chi!)
  54.     FOR M%% = 0 TO 2
  55.         IF RND > 0.5 THEN ChlorinePos!(N%%, M%%) = -ChlorinePos!(N%%, M%%)
  56.         ChlorineVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  57.         SodiumVel!(N%%, M%%) = (RND - 0.5) * Kelvin!
  58.     NEXT M%%
  59.     Chi! = 2 * _PI * RND
  60.     Psi! = _PI * RND
  61.     SodiumPos!(N%%, 2) = ChlorinePos!(N%%, 2) + Atom! * SIN(Psi!) * COS(Chi!)
  62.     SodiumPos!(N%%, 0) = ChlorinePos!(N%%, 0) + Atom! * SIN(Psi!) * SIN(Chi!)
  63.     SodiumPos!(N%%, 1) = ChlorinePos!(N%%, 1) + Atom! * COS(Psi!)
  64. NEXT N%%
  65.  
  66. ' Ball Colours (Cyperium Method)
  67. DATA 0,0,255
  68. DATA 255,0,0
  69. DATA 217,163,173
  70. DATA 0,200,200
  71. FOR N%% = 0 TO 3
  72.     FOR P%% = 0 TO 2
  73.         READ BallStats%(N%%, P%%)
  74.     NEXT P%%
  75.     TempImage& = _NEWIMAGE(256, 256, 32)
  76.     _DEST TempImage&
  77.     COLOR _RGBA(BallStats%(N%%, 0), BallStats%(N%%, 1), BallStats%(N%%, 2), 65), _RGBA(0, 0, 0, 0)
  78.     'Image data goes from 1 to 255 (not 0 to 255)
  79.     FOR Z% = 128 TO 255
  80.         FOR X% = 1 TO 255
  81.             FOR Y% = 1 TO 255
  82.                 DeltaX% = X% - 127
  83.                 DeltaY% = Y% - 127
  84.                 DeltaZ% = Z% - 127
  85.                 Dist! = SQR((DeltaX% * DeltaX%) + (DeltaY% * DeltaY%) + (DeltaZ% * DeltaZ%))
  86.                 IF Dist! > 125 AND Dist! < 127 THEN PSET (X%, Y%), _RGBA(CINT(Z% * BallStats%(N%%, 0) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 1) * (1 - (XBright! * X% / 255)) / 255), CINT(Z% * BallStats%(N%%, 2) * (1 - (XBright! * X% / 255)) / 255), 65)
  87.             NEXT
  88.         NEXT
  89.     NEXT
  90.     IF N%% = 0 THEN
  91.         Sodium& = _COPYIMAGE(TempImage&, 33)
  92.     ELSEIF N%% = 1 THEN
  93.         Chlorine& = _COPYIMAGE(TempImage&, 33)
  94.     ELSEIF N%% = 2 THEN
  95.         Pink& = _COPYIMAGE(TempImage&, 33)
  96.     ELSE
  97.         Cyan& = _COPYIMAGE(TempImage&, 33)
  98.     END IF
  99.     _FREEIMAGE TempImage&
  100. NEXT N%%
  101.  
  102. 'Images
  103. TempImage& = _NEWIMAGE(102, 52, 32)
  104. _DEST TempImage&
  105. LINE (0, 0)-(101, 51), _RGB32(255, 255, 255), BF
  106. LineImage& = _COPYIMAGE(TempImage&, 33)
  107. _FREEIMAGE TempImage&
  108. TempImage& = _NEWIMAGE(80, 100, 32)
  109. _DEST TempImage&
  110. COLOR _RGB32(150, 150, 150), _RGB32(80, 80, 80)
  112. _PRINTSTRING (20, 40), "Pause"
  113. Pause& = _COPYIMAGE(TempImage&, 33)
  114. _FREEIMAGE TempImage&
  115. TempImage& = _NEWIMAGE(80, 100, 32)
  116. _DEST TempImage&
  117. COLOR _RGB32(150, 150, 150), _RGB32(80, 80, 80)
  119. _PRINTSTRING (8, 40), "Continue"
  120. Continue& = _COPYIMAGE(TempImage&, 33)
  121. _FREEIMAGE TempImage&
  122. TempImage& = _NEWIMAGE(80, 100, 32)
  123. _DEST TempImage&
  124. COLOR _RGB32(150, 150, 150), _RGB32(80, 80, 80)
  126. _PRINTSTRING (20, 30), "Draw"
  127. _PRINTSTRING (20, 60), "Bonds"
  128. Bonds& = _COPYIMAGE(TempImage&, 33)
  129. _FREEIMAGE TempImage&
  130. TempImage& = _NEWIMAGE(80, 100, 32)
  131. _DEST TempImage&
  132. COLOR _RGB32(150, 150, 150), _RGB32(80, 80, 80)
  134. _PRINTSTRING (20, 25), "Don't"
  135. _PRINTSTRING (20, 45), "Draw"
  136. _PRINTSTRING (20, 65), "Bonds"
  137. NoBonds& = _COPYIMAGE(TempImage&, 33)
  138. _FREEIMAGE TempImage&
  139. TempImage& = _NEWIMAGE(80, 100, 32)
  140. _DEST TempImage&
  141. COLOR _RGB32(150, 150, 150), _RGB32(80, 80, 80)
  143. _PRINTSTRING (24, 40), "Quit"
  144. Quit& = _COPYIMAGE(TempImage&, 33)
  145.  
  146. 'Create screen
  147. SCREEN _NEWIMAGE(ScreenX%, ScreenY%, 32)
  151.  
  152. 'Run simulation
  153. NoBalls%% = NoSeed%%
  154. Count% = 0
  155. ViewAngle! = _PI * (1 - RND)
  156. DrawBonds` = False
  157. Paused` = False
  158. ASaltyDog` = True
  159. WHILE ASaltyDog`
  160.     _LIMIT 25
  161.     CALL CentreOfMass
  162.     'Mouse Input
  164.         XMouse% = _MOUSEX: YMouse% = _MOUSEY
  165.         IF _MOUSEBUTTON(1) THEN '2 for LH Mouse
  166.             IF XMouse% > ScreenX% - 199 AND XMouse% < ScreenX% - 121 AND YMouse% > 21 AND YMouse% < 119 THEN
  167.                 IF DrawBonds` THEN
  168.                     DrawBonds` = False
  169.                 ELSE
  170.                     DrawBonds` = True
  171.                 END IF
  172.             ELSEIF XMouse% > ScreenX% - 99 AND XMouse% < ScreenX% - 21 AND YMouse% > 21 AND YMouse% < 119 THEN
  173.                 IF Paused` THEN
  174.                     Paused` = False
  175.                 ELSE
  176.                     Paused` = True
  177.                 END IF
  178.             ELSEIF XMouse% > ScreenX% - 99 AND XMouse% < ScreenX% - 21 AND YMouse% > ScreenY% - 119 AND YMouse% < ScreenY% - 21 THEN
  179.                 ASaltyDog` = False
  180.             END IF
  181.         END IF
  182.     WEND
  183.     'Display atoms and calculate forces
  184.     MaxDist! = 0
  185.     F1! = 900 + 100 * ((NoBalls%% - NoSeed%%) / (TotBalls%% - NoSeed%%))
  186.     FOR N%% = 0 TO NoBalls%% - 1
  187.         XTemp! = XDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2))): ZTemp! = ZDash!((ChlorinePos!(N%%, 0)), (ChlorinePos!(N%%, 2)))
  188.         IF N%% <= NoSeed%% - 1 THEN
  189.             _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Chlorine& TO(-(ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  190.             _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Chlorine& TO((ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  191.         ELSE
  192.             _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Pink& TO(-(ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  193.             _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Pink& TO((ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-(-(ChlorineSize%% - 1) \ 2 + XTemp!, -(ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)-((ChlorineSize%% - 1) \ 2 + XTemp!, (ChlorineSize%% - 1) \ 2 + ChlorinePos!(N%%, 1), ZTemp! - Offset%)
  194.         END IF
  195.         XTemp! = XDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2))): ZTemp! = ZDash!((SodiumPos!(N%%, 0)), (SodiumPos!(N%%, 2)))
  196.         IF N%% <= NoSeed%% - 1 THEN
  197.             _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Sodium& TO(-(SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  198.             _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Sodium& TO((SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  199.         ELSE
  200.             _MAPTRIANGLE (0, 0)-(255, 0)-(0, 255), Cyan& TO(-(SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  201.             _MAPTRIANGLE (255, 255)-(0, 255)-(255, 0), Cyan& TO((SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-(-(SodiumSize%% - 1) \ 2 + XTemp!, -(SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)-((SodiumSize%% - 1) \ 2 + XTemp!, (SodiumSize%% - 1) \ 2 + SodiumPos!(N%%, 1), ZTemp! - Offset%)
  202.         END IF
  203.         FOR M%% = 0 TO 2
  204.             SodiumAcc!(N%%, M%%) = 0
  205.         NEXT M%%
  206.         FOR M%% = 0 TO 2
  207.             ChlorineAcc!(N%%, M%%) = 0
  208.         NEXT M%%
  209.         FOR L%% = 0 TO NoBalls%% - 1
  210.             'opposites
  211.             D! = SQR((SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (SodiumPos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (SodiumPos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (SodiumPos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  212.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  213.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  214.             FOR M%% = 0 TO 2
  215.                 SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  216.             NEXT M%%
  217.             IF D! < 0.9 * Atom! AND DrawBonds` THEN _MAPTRIANGLE (0, 0)-(101, 0)-(101, 51), LineImage& TO(XDash!(SodiumPos!(N%%, 0), SodiumPos!(N%%, 2)), SodiumPos!(N%%, 1), ZDash!(SodiumPos!(N%%, 0), SodiumPos!(N%%, 2)) - Offset%)-(XDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)), ChlorinePos!(L%%, 1), ZDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)) - Offset%)-(XDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)), ChlorinePos!(L%%, 1), ZDash!(ChlorinePos!(L%%, 0), ChlorinePos!(L%%, 2)) - Offset% - 1), , _SMOOTH
  218.             D! = SQR((SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) * (SodiumPos!(L%%, 0) - ChlorinePos!(N%%, 0)) + (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) * (SodiumPos!(L%%, 1) - ChlorinePos!(N%%, 1)) + (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)) * (SodiumPos!(L%%, 2) - ChlorinePos!(N%%, 2)))
  219.             F! = (Attraction!(D!) + Repulsion!(D!)) / F1!
  220.             'IF F! < FMin! / F1! THEN F! = FMin! / F1!
  221.             FOR M%% = 0 TO 2
  222.                 ChlorineAcc!(N%%, M%%) = F! * (SodiumPos!(L%%, M%%) - ChlorinePos!(N%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  223.             NEXT M%%
  224.             IF L%% <> N%% THEN
  225.                 'same type
  226.                 D! = SQR((SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) * (SodiumPos!(N%%, 0) - SodiumPos!(L%%, 0)) + (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) * (SodiumPos!(N%%, 1) - SodiumPos!(L%%, 1)) + (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)) * (SodiumPos!(N%%, 2) - SodiumPos!(L%%, 2)))
  227.                 F! = -(Attraction!(D!)) / F2!
  228.                 FOR M%% = 0 TO 2
  229.                     SodiumAcc!(N%%, M%%) = -F! * (SodiumPos!(N%%, M%%) - SodiumPos!(L%%, M%%)) / D! + SodiumAcc!(N%%, M%%)
  230.                 NEXT M%%
  231.                 D! = SQR((ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) * (ChlorinePos!(N%%, 0) - ChlorinePos!(L%%, 0)) + (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) * (ChlorinePos!(N%%, 1) - ChlorinePos!(L%%, 1)) + (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)) * (ChlorinePos!(N%%, 2) - ChlorinePos!(L%%, 2)))
  232.                 F! = -(Attraction!(D!)) / F2!
  233.                 FOR M%% = 0 TO 2
  234.                     ChlorineAcc!(N%%, M%%) = -F! * (ChlorinePos!(N%%, M%%) - ChlorinePos!(L%%, M%%)) / D! + ChlorineAcc!(N%%, M%%)
  235.                 NEXT M%%
  236.             END IF
  237.         NEXT L%%
  238.         'Pause
  239.         IF NOT Paused` THEN
  240.             FOR M%% = 0 TO 2
  241.                 SodiumPos!(N%%, M%%) = SodiumPos!(N%%, M%%) + SodiumVel!(N%%, M%%)
  242.                 ChlorinePos!(N%%, M%%) = ChlorinePos!(N%%, M%%) + ChlorineVel!(N%%, M%%)
  243.                 SodiumVel!(N%%, M%%) = SodiumVel!(N%%, M%%) + SodiumAcc!(N%%, M%%)
  244.                 IF ABS(SodiumVel!(N%%, M%%)) > Kelvin! THEN SodiumVel!(N%%, M%%) = Kelvin! * (ABS(SodiumVel!(N%%, M%%)) / SodiumVel!(N%%, M%%))
  245.                 ChlorineVel!(N%%, M%%) = ChlorineVel!(N%%, M%%) + ChlorineAcc!(N%%, M%%)
  246.                 IF ABS(ChlorineVel!(N%%, M%%)) > Kelvin! THEN ChlorineVel!(N%%, M%%) = Kelvin! * (ABS(ChlorineVel!(N%%, M%%)) / ChlorineVel!(N%%, M%%))
  247.             NEXT M%%
  248.         END IF
  249.     NEXT N%%
  250.     'Pause/Adjust for orthogonal forces
  251.     IF NOT Paused` THEN
  252.         _PUTIMAGE (ScreenX% - 100, 20), Pause&
  253.         FOR N%% = 0 TO NoBalls%% - 1
  254.             FOR M%% = 0 TO 5 'the six orthogonal positions from each sodium atom
  255.                 CALL Orthogonal(N%%, M%%) 'Move chlorine atom
  256.             NEXT M%%
  257.         NEXT N%%
  258.         ViewAngle! = ViewAngle! + 0.008
  259.         IF ViewAngle! > _PI THEN ViewAngle! = ViewAngle! - 2 * _PI
  260.         IF NoBalls%% < TotBalls%% THEN Count% = Count% + 1
  261.         IF NoBalls%% = NoSeed%% THEN
  262.             IF Count% >= 2000 AND ((ViewAngle! > -0.05 AND ViewAngle! < 0.05) OR (ViewAngle! > -_PI - 0.05 AND ViewAngle! < 0.05 - _PI)) THEN
  263.                 NoBalls%% = NoBalls%% + 2
  264.                 Count% = 0
  265.             END IF
  266.             'might try the angle of the next ball, not just viewing angle - future version
  267.         ELSEIF Count% >= 100 AND NoBalls%% < TotBalls% AND ((ViewAngle! > -0.05 AND ViewAngle! < 0.05) OR (ViewAngle! > -_PI - 0.05 AND ViewAngle! < 0.05 - _PI)) THEN
  268.             NoBalls%% = NoBalls%% + 2
  269.             Count% = 0
  270.         END IF
  271.     ELSE
  272.         _PUTIMAGE (ScreenX% - 100, 20), Continue&
  273.     END IF
  274.     'Draw Bonds
  275.     IF NOT DrawBonds` THEN
  276.         _PUTIMAGE (ScreenX% - 200, 20), Bonds&
  277.     ELSE
  278.         _PUTIMAGE (ScreenX% - 200, 20), NoBonds&
  279.     END IF
  280.     _PUTIMAGE (ScreenX% - 100, ScreenY% - 120), Quit&
  281.     LOCATE 1, 1: PRINT NoBalls%%;
  282.     _DISPLAY
  283.     IF INKEY$ <> "" THEN ASaltyDog` = False
  285.  
  287.  
  288. FUNCTION Attraction! (Dist!)
  289.     Attraction! = A0! * (1 / (Dist! / A2!) ^ A1!)
  291.  
  292. FUNCTION Repulsion! (Dist!)
  293.     Repulsion! = -R0! * (1 / (Dist! / R2!) ^ R1!)
  295.  
  296. FUNCTION XDash! (X!, Z!)
  297.     XDash! = X! * COS(ViewAngle!) + Z! * SIN(ViewAngle!)
  299.  
  300. FUNCTION ZDash! (X!, Z!)
  301.     ZDash! = -X! * SIN(ViewAngle!) + Z! * COS(ViewAngle!)
  303.  
  304. SUB Orthogonal (P%%, Q%%)
  305.     OnlyOneChlorine%% = True
  306.     NoChlorines%% = 0
  307.     R%% = 0
  308.     WHILE R%% <= NoBalls%% - 1 AND OnlyOneChlorine%%
  309.         IF R%% <> P%% THEN
  310.             Sepn! = SQR((SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)) * (SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)) + (SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)) * (SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)) + (SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)) * (SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)))
  311.             IF Sepn! < Atom! THEN
  312.                 X! = SodiumPos!(R%%, 0) - SodiumPos!(P%%, 0)
  313.                 Y! = SodiumPos!(R%%, 1) - SodiumPos!(P%%, 1)
  314.                 Z! = SodiumPos!(R%%, 2) - SodiumPos!(P%%, 2)
  315.                 SELECT CASE Q%%
  316.                     CASE 0
  317.                         S1! = SQR(Y! * Y! + Z! * Z!)
  318.                         Theta! = _ATAN2(S1!, X!)
  319.                         IF X! > 0 AND X! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  320.                     CASE 1
  321.                         S1! = SQR(X! * X! + Z! * Z!)
  322.                         Theta! = _ATAN2(S1!, Y!)
  323.                         IF Y! > 0 AND Y! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  324.                     CASE 2
  325.                         S1! = SQR(Y! * Y! + X! * X!)
  326.                         Theta! = _ATAN2(S1!, Z!)
  327.                         IF Z! > 0 AND Z! < Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  328.                     CASE 3
  329.                         S1! = SQR(Y! * Y! + Z! * Z!)
  330.                         Theta! = _ATAN2(S1!, -X!)
  331.                         IF X! < 0 AND X! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  332.                     CASE 4
  333.                         S1! = SQR(X! * X! + Z! * Z!)
  334.                         Theta! = _ATAN2(S1!, -Y!)
  335.                         IF Y! < 0 AND Y! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  336.                     CASE ELSE '5
  337.                         S1! = SQR(Y! * Y! + X! * X!)
  338.                         Theta! = _ATAN2(S1!, -Z!)
  339.                         IF Z! < 0 AND Z! > -Atom! AND ABS(Theta!) < ThetaMax! THEN OnlyOneChlorine%% = False
  340.                 END SELECT
  341.             END IF
  342.         END IF
  343.         IF OnlyOneChlorine%% THEN
  344.             Sepn! = SQR((ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)) * (ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)) + (ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)) * (ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)) + (ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)) * (ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)))
  345.             IF Sepn! < Atom! THEN
  346.                 X! = ChlorinePos!(R%%, 0) - SodiumPos!(P%%, 0)
  347.                 Y! = ChlorinePos!(R%%, 1) - SodiumPos!(P%%, 1)
  348.                 Z! = ChlorinePos!(R%%, 2) - SodiumPos!(P%%, 2)
  349.                 SELECT CASE Q%%
  350.                     CASE 0
  351.                         S1! = SQR(Y! * Y! + Z! * Z!)
  352.                         Theta! = _ATAN2(S1!, X!)
  353.                         IF X! > 0 AND X! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  354.                             NoChlorines%% = NoChlorines%% + 1
  355.                             ROne%% = R%%
  356.                         END IF
  357.                     CASE 1
  358.                         S1! = SQR(X! * X! + Z! * Z!)
  359.                         Theta! = _ATAN2(S1!, Y!)
  360.                         IF Y! > 0 AND Y! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  361.                             NoChlorines%% = NoChlorines%% + 1
  362.                             ROne%% = R%%
  363.                         END IF
  364.                     CASE 2
  365.                         S1! = SQR(Y! * Y! + X! * X!)
  366.                         Theta! = _ATAN2(S1!, Z!)
  367.                         IF Z! > 0 AND Z! < Atom! AND ABS(Theta!) < ThetaMax! THEN
  368.                             NoChlorines%% = NoChlorines%% + 1
  369.                             ROne%% = R%%
  370.                         END IF
  371.                     CASE 3
  372.                         S1! = SQR(Y! * Y! + Z! * Z!)
  373.                         Theta! = _ATAN2(S1!, -X!)
  374.                         IF X! < 0 AND X! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  375.                             NoChlorines%% = NoChlorines%% + 1
  376.                             ROne%% = R%%
  377.                         END IF
  378.                     CASE 4
  379.                         S1! = SQR(X! * X! + Z! * Z!)
  380.                         Theta! = _ATAN2(S1!, -Y!)
  381.                         IF Y! < 0 AND Y! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  382.                             NoChlorines%% = NoChlorines%% + 1
  383.                             ROne%% = R%%
  384.                         END IF
  385.                     CASE ELSE '5
  386.                         S1! = SQR(Y! * Y! + X! * X!)
  387.                         Theta! = _ATAN2(S1!, -Z!)
  388.                         IF Z! < 0 AND Z! > -Atom! AND ABS(Theta!) < ThetaMax! THEN
  389.                             NoChlorines%% = NoChlorines%% + 1
  390.                             ROne%% = R%%
  391.                         END IF
  392.                 END SELECT
  393.                 IF NoChlorines%% > 1 THEN OnlyOneChlorine%% = False
  394.             END IF
  395.         END IF
  396.         R%% = R%% + 1
  397.     WEND
  398.     IF NoChlorines%% = 0 THEN OnlyOneChlorine%% = False
  399.     IF OnlyOneChlorine%% THEN
  400.         'Move Chlorine Atom
  401.         X! = ChlorinePos!(ROne%%, 0) - SodiumPos!(P%%, 0)
  402.         Y! = ChlorinePos!(ROne%%, 1) - SodiumPos!(P%%, 1)
  403.         Z! = ChlorinePos!(ROne%%, 2) - SodiumPos!(P%%, 2)
  404.         SELECT CASE Q%%
  405.             CASE 0, 3
  406.                 ChlorinePos!(ROne%%, 1) = ChlorinePos!(ROne%%, 1) - Y! * (1 - Xstal!)
  407.                 ChlorinePos!(ROne%%, 2) = ChlorinePos!(ROne%%, 2) - Z! * (1 - Xstal!)
  408.             CASE 1, 4
  409.                 ChlorinePos!(ROne%%, 0) = ChlorinePos!(ROne%%, 0) - X! * (1 - Xstal!)
  410.                 ChlorinePos!(ROne%%, 2) = ChlorinePos!(ROne%%, 2) - Z! * (1 - Xstal!)
  411.             CASE 2, 5
  412.                 ChlorinePos!(ROne%%, 0) = ChlorinePos!(ROne%%, 0) - X! * (1 - Xstal!)
  413.                 ChlorinePos!(ROne%%, 1) = ChlorinePos!(ROne%%, 1) - Y! * (1 - Xstal!)
  414.         END SELECT
  415.     END IF
  417.  
  418. SUB CentreOfMass 'centre on original seed atoms
  419.     TotMass! = 0
  420.     MRx! = 0: MRy! = 0: MRz! = 0
  421.     Px! = 0: Py! = 0: Pz! = 0
  422.     FOR N% = 0 TO NoSeed%% - 1
  423.         TotMass! = TotMass! + 1
  424.         MRx! = MRx! + SodiumPos!(N%, 0)
  425.         MRy! = MRy! + SodiumPos!(N%, 1)
  426.         MRz! = MRz! + SodiumPos!(N%, 2)
  427.         Px! = SodiumVel!(N%, 0) + Px!
  428.         Py! = SodiumVel!(N%, 1) + Py!
  429.         Pz! = SodiumVel!(N%, 2) + Pz!
  430.         TotMass! = TotMass! + 1
  431.         MRx! = MRx! + ChlorinePos!(N%, 0)
  432.         MRy! = MRy! + ChlorinePos!(N%, 1)
  433.         MRz! = MRz! + ChlorinePos!(N%, 2)
  434.         Px! = ChlorineVel!(N%, 0) + Px!
  435.         Py! = ChlorineVel!(N%, 1) + Py!
  436.         Pz! = ChlorineVel!(N%, 2) + Pz!
  437.     NEXT N%
  438.     FOR N% = 0 TO NoSeed%% - 1
  439.         SodiumPos!(N%, 0) = SodiumPos!(N%, 0) - (MRx! / TotMass!)
  440.         SodiumPos!(N%, 1) = SodiumPos!(N%, 1) - (MRy! / TotMass!)
  441.         SodiumPos!(N%, 2) = SodiumPos!(N%, 2) - (MRz! / TotMass!)
  442.         SodiumVel!(N%, 0) = SodiumVel!(N%, 0) - (Px! / TotMass!)
  443.         SodiumVel!(N%, 1) = SodiumVel!(N%, 1) - (Py! / TotMass!)
  444.         SodiumVel!(N%, 2) = SodiumVel!(N%, 2) - (Pz! / TotMass!)
  445.         ChlorinePos!(N%, 0) = ChlorinePos!(N%, 0) - (MRx! / TotMass!)
  446.         ChlorinePos!(N%, 1) = ChlorinePos!(N%, 1) - (MRy! / TotMass!)
  447.         ChlorinePos!(N%, 2) = ChlorinePos!(N%, 2) - (MRz! / TotMass!)
  448.         ChlorineVel!(N%, 0) = ChlorineVel!(N%, 0) - (Px! / TotMass!)
  449.         ChlorineVel!(N%, 1) = ChlorineVel!(N%, 1) - (Py! / TotMass!)
  450.         ChlorineVel!(N%, 2) = ChlorineVel!(N%, 2) - (Pz! / TotMass!)
  451.     NEXT N%
  453.  
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