[017]異種金属結晶の接触

 投稿者：mike  投稿日：2017年 6月19日(月)10時12分40秒
  Morseポテンシャルによる異種金属結晶の接触の分子動力学法プログラム017mixMMD2D.basを公開します。
異なった種類のナノ結晶を接触させます。接触すると表面エネルギーを解放し、温度が高くなります。
一般に表面エネルギー（Morseポテンシャルの場合は解離エネルギーに相当）の大きい方の表面に
小さい方の原子が覆う形が安定になります。

表示の説明：
鉄原子は暗い水色、アルミニウム原子は茶色の円であらわします。
表示は[D]のキーを押すことで変更できます。

試験環境：
本プログラムは十進BASIC 6.6.3.1 / macOS 10.7.5, 十進BASIC Ver 7.8.0 / windows 10　でテストしました。


---------------------


!
! ========= molecular dynamics 2D - Morse potential ==========
!
! 017mixMMD2D.bas
!   Copyright(C) 2017 Mitsuru Ikeuchi
!
! ver 0.0.0  2017.04.22  created
! ver 0.0.1  2017.06.11  bug fixed
!
OPTION ARITHMETIC NATIVE
DECLARE EXTERNAL SUB mmd2d.setInitialCondition, mmd2d.moveParticles, mmd2d.drawParticles
DECLARE EXTERNAL FUNCTION INKEY$
LET tempMode = 0    !tempMode: 0:adiabatic  1:constant temperature
LET contTemp = 300  !contTemp: controled constant temperature(K)
LET drawMode = 0    !drawMode: 0:bond  1:circle+bond 2:velocitySpace
DIM menu$(8)
LET menu$(1) = "Fe Al"
LET menu$(2) = "Fe Mo"
LET menu$(3) = "Fe Hg"
LET menu$(4) = "W Pb"
LET menu$(5) = "Ni Cr"
LET menu$(6) = "Ag Cu"
LET menu$(7) = "Al Ar"
LET menu$(8) = "continue"

!setInitialCondition(kind1,kind2,boxSizeInNM,contTemp)
!molKind: 0:W 1:Mo 2:Cr 3:Fe 4:Ni 5:Al 6:Pb 7:Cu 8:Ag 17:Ar 20:Hg
CALL setInitialCondition(3,5,6.0,contTemp)

DO
   CALL moveParticles(tempMode,contTemp)
   CALL drawParticles(tempMode,contTemp,drawMode)
   LET S$=INKEY$
   IF S$="0" THEN
      LOCATE VALUE (1),RANGE 0 TO 4000 : temp
      IF temp>1 THEN
         LET tempMode = 1
         LET contTemp = temp
      ELSE
         LET tempMode = 0
      END IF
   ELSEIF S$="D" OR S$="d" THEN
      LET drawMode = MOD(drawMode+1,3)
   ELSEIF S$="9" THEN
      LOCATE CHOICE (menu$) :nmenu
      IF nmenu=1 THEN      !--- Fe Al box=6x6nm
         CALL setInitialCondition(3,5,6.0,contTemp)
      ELSEIF nmenu=2 THEN  !--- Fe Mo
         CALL setInitialCondition(3,1,6.0,contTemp)
      ELSEIF nmenu=3 THEN  !--- Fe Hg
         CALL setInitialCondition(3,20,6.0,contTemp)
      ELSEIF nmenu=4 THEN  !--- W Pb
         CALL setInitialCondition(0,6,6.0,contTemp)
      ELSEIF nmenu=5 THEN  !--- Ni Cr
         CALL setInitialCondition(4,2,6.0,contTemp)
      ELSEIF nmenu=6 THEN  !--- Ag Cu
         CALL setInitialCondition(8,7,6.0,contTemp)
      ELSEIF nmenu=7 THEN  !--- Al Ar
         CALL setInitialCondition(5,17,6.0,contTemp)
      ELSEIF nmenu=8 THEN  !contine
      END IF
   END IF
LOOP UNTIL S$=CHR$(27)
END


EXTERNAL FUNCTION INKEY$  !from decimalBASIC library
OPTION ARITHMETIC NATIVE
SET ECHO "OFF"
LET S$=""
CHARACTER INPUT NOWAIT: S$
LET INKEY$=S$
END FUNCTION

! ---------- molecular dynamics 2D - Morse potential ----------
!
!  method: velocity Verlet algorithm
!    (1) vi = vi + (Fi/mi)*(0.5dt)
!    (2) ri = ri + vi*dt
!    (3) calculation Fi <- {r1,r2,...,rn} Fi=sum(Fij,j=1 to n),Fij=F(ri-rj)
!    (4) vi = vi + (Fi/mi)*(0.5dt)
!    (6) goto (1)
!  potential: Morse V(r) = D*((1-EXP(-A*(r-r0)))^2-1)
!                        = D*(EXP(-2*A*(r-r0))-2*EXP(-A*(r-r0)))
!    (D:dissociation energy, r0:bond length, A:width parameter { A=SQR(k/(2*D)) }
!             force F(r) = -dV(r)/dr
!                        = 2*D*A*y*(y-1), y=EXP(-A*(r-r0))
MODULE mmd2d
MODULE OPTION ARITHMETIC NATIVE
PUBLIC SUB setInitialCondition !(molKind,boxSizeInNM,xtalSizeInNM,contTemp)
PUBLIC SUB moveParticles !(tempMode,contTemp)
PUBLIC SUB drawParticles !(drawMode:0:realSpace 1:velocitySpace)
SHARE NUMERIC molecKind1,molecKind2, sysTime, dt, nMolec, xMax, yMax, rCutoff, hh
SHARE NUMERIC xx(500),yy(500)           ! (xx(i),yy(i))  : position of i-th particle
SHARE NUMERIC vx(500),vy(500)           ! (vx(i),vy(i))  : velocity of i-th particle
SHARE NUMERIC ffx(500),ffy(500)         ! (ffx(i),ffy(i)): total force of i-th particle
SHARE NUMERIC kind(500),mas(500)        ! kind(i),mas(i) : molec kind, mass of i-th particle
SHARE NUMERIC reg(500,0 TO 100)         ! register near molec reg(i,0):number of near i-th molec
SHARE NUMERIC molecData(0 TO 20,0 TO 3) ! molecule 0:mass, 1:epsilon, 2:sigma, 3:dt
SHARE STRING molecSTR$(0 TO 20)         ! molec string
SHARE NUMERIC forceTable(0 TO 20, 0 TO 20,0 TO 1001) ! force table

LET molecKind1 = 3         ! molecule kind1 - 3:Fe
LET molecKind2 = 1         ! molecule kind2 - 1:Mo
LET sysTime = 0.0          ! system time (s) in the module
LET dt = 5.0*1.0e-15       ! time step (s)
LET nMolec = 100           ! number of particles
LET xMax = 6.0E-9          ! x-Box size (m)
LET yMax = 6.0E-9          ! y-Box size (m)
LET rCutoff = 1.0e-9       ! force cutoff radius (m)
LET hh = 1e-12             ! force table step (m)
LET molecData(0,0)=0       ! if molecData(0,0)=0 then set molecData(,)

! ---------- set initial condition

EXTERNAL SUB setInitialCondition(kind1,kind2,boxSizeInNM,contTemp)
   DECLARE EXTERNAL SUB setMolecData,setMolecules,ajustVelocity,setForceTable
   DECLARE EXTERNAL FUNCTION setCrystalBlock
   RANDOMIZE
   CALL setMolecData
   LET molecKind1 = kind1
   LET molecKind2 = kind2
   LET sysTime = 0.0
   LET xMax = boxSizeInNM*1.0e-9
   LET yMax = boxSizeInNM*1.0e-9
   ! set particles
   LET s = 0.1*xMax
   LET xtalSize = 0.35*xMax
   LET ss = 0.55*xMax
   LET ii = setCrystalBlock(1, kind1, s, s, xtalSize, xtalSize, PI/4)
   LET ii = setCrystalBlock(ii+1, kind2, s, ss, xtalSize, xtalSize, 0)
   LET ii = setCrystalBlock(ii+1, kind2, ss, s, xtalSize, xtalSize, 0)
   LET nMolec = setCrystalBlock(ii+1, kind1, ss, ss, xtalSize, xtalSize, 0)
   CALL ajustVelocity(contTemp)
   LET rCutoff = MIN(1.0e-9, 3.0*MAX(molecData(kind1,3),molecData(kind2,3)))
   CALL setForceTable
   SET COLOR MIX(240) 1.0,0.2,0.2 !for bond direction color
   SET COLOR MIX(241) 0.6,0.6,0.0
   SET COLOR MIX(242) 0.0,1.0,0.0
   SET COLOR MIX(243) 0.0,0.6,0.6
   SET COLOR MIX(244) 0.2,0.2,1.0
   SET COLOR MIX(245) 0.8,0.0,0.8
   ! set window
   SET WINDOW 0,500,0,500
END SUB

EXTERNAL SUB setMolecData
! Morse potential data
!       0:mass(AU) 1:D(eV)  2:A(m^-1)  3:r0(m)
   DATA   183.85 , 0.9906, 1.4116e10, 3.032e-10 !  0 W
   DATA    95.94 , 0.8032, 1.5079e10, 2.976e-10 !  1 Mo
   DATA    51.996, 0.4414, 1.5721e10, 2.754e-10 !  2 Cr
   DATA    55.847, 0.4174, 1.3885e10, 2.845e-10 !  3 Fe
   DATA    58.71 , 0.4205, 1.4199e10, 2.780e-10 !  4 Ni
   DATA    26.98 , 0.2703, 1.1646e10, 3.253e-10 !  5 Al
   DATA   207.19 , 0.2348, 1.1836e10, 3.733e-10 !  6 Pb
   DATA    63.54 , 0.3429, 1.3588e10, 2.866e-10 !  7 Cu
   DATA   107.87 , 0.3323, 1.3690e10, 3.115e-10 !  8 Ag
   DATA    40.08 , 0.1623, 0.8054e10, 4.569e-10 !  9 Ca
   DATA    87.62 , 0.1513, 0.7878e10, 4.988e-10 ! 10 Sr
   DATA   137.34 , 0.1416, 0.6570e10, 5.373e-10 ! 11 Ba
   DATA    22.99 , 0.0633, 0.5900e10, 5.336e-10 ! 12 Na
   DATA    39.102, 0.0542, 0.4977e10, 6.369e-10 ! 13 K
   DATA    85.47 , 0.0464, 0.4298e10, 7.207e-10 ! 14 Rb
   DATA   132.905, 0.0449, 0.4157e10, 7.557e-10 ! 15 Cs
   DATA    20.183, 0.0031, 1.6500e10, 3.076e-10 ! 16 Ne
   DATA    39.948, 0.0104, 1.3400e10, 3.816e-10 ! 17 Ar
   DATA    83.80 , 0.0141, 1.2500e10, 4.097e-10 ! 18 Kr
   DATA   131.30 , 0.0200, 1.2400e10, 4.467e-10 ! 19 Xe
   DATA   200.59 , 0.0734, 1.4900e10, 3.255e-10 ! 20 Hg
   DATA "W" ,"Mo","Cr","Fe","Ni","Al","Pb","Cu","Ag","Ca","Sr"
   DATA "Ba","Na","K" ,"Rb","Cs","Ne","Ar","Kr","Xe","Hg"

   IF molecData(0,0)=0 THEN
      MAT READ molecData
      FOR i=0 TO 20
         LET molecData(i,0) = molecData(i,0)*1.661e-27 !mass(AU)--> (kg)
         LET molecData(i,1) = molecData(i,1)*1.602e-19 !eps(eV) --> (J)
      NEXT i
      MAT READ molecSTR$
   END IF
END SUB

EXTERNAL SUB setGas(nMolecule)
   DECLARE EXTERNAL SUB ajustVelocity
   LET r0 = molecData(knd,3)
   FOR j=1 TO nMolecule
      LET loopCount = 0
      DO
         LET xx(j) = (xMax-2*r0)*RND + r0
         LET yy(j) = (yMax-2*r0)*RND + r0
         FOR i=1 TO j-1
            IF (xx(i)-xx(j))^2+(yy(i)-yy(j))^2 < 2*r0^2 THEN EXIT FOR
         NEXT i
         LET loopCount = loopCount + 1
         IF loopCount>1000 THEN EXIT DO
      LOOP UNTIL i>=j
      IF loopCount>1000 THEN
         LET nMolec = j - 1
         EXIT FOR
      END IF
   NEXT j
   FOR i=1 TO nMolec
      LET vx(i) = 200.0*(RND+RND+RND+RND+RND+RND-3)
      LET vy(i) = 200.0*(RND+RND+RND+RND+RND+RND-3)
      LET ffx(i) = 0.0
      LET ffy(i) = 0.0
   NEXT i
END SUB

EXTERNAL FUNCTION setCrystalBlock(ii, knd, x0, y0, xLen, yLen, theta)
   DECLARE EXTERNAL SUB setParticle
   LET iip = ii
   LET a = 0.98*molecData(knd,3) !r0 of knd
   LET b = 0.866025*a
   LET leng = xLen
   IF (leng<yLen) THEN LET leng = yLen
   LET leng = 1.5*leng
   LET nx = INT(leng/b) + 1
   LET ny = INT(leng/a) + 1
   LET sth = SIN(theta)
   LET cth = COS(theta)
   FOR i=0 TO nx-1
      LET x = b*i - leng/2.0
      FOR j=0 TO ny-1
         LET y = a*j - leng/2.0
         IF MOD(i,2)=1 THEN LET y = y + 0.5*a
         LET xp = x0 + xLen/2.0 + cth*x - sth*y
         LET yp = y0 + yLen/2.0 + sth*x + cth*y
         IF (xp>=x0 AND xp<=x0+xLen AND yp>=y0 AND yp<=y0+yLen) THEN
            CALL setParticle(iip, knd, xp, yp)
            LET iip = iip + 1
         END IF
      NEXT j
   NEXT i
   LET setCrystalBlock = iip - 1
end function

EXTERNAL SUB setParticle(i, knd, x, y)
   LET xx(i) = x
   LET yy(i) = y
   LET vx(i) = 200.0*(RND+RND+RND+RND+RND+RND-3)
   LET vy(i) = 200.0*(RND+RND+RND+RND+RND+RND-3)
   LET ffx(i) = 0.0
   LET ffy(i) = 0.0
   LET mas(i) = molecData(knd,0)
   LET kind(i) = knd
END SUB

EXTERNAL SUB setForceTable
   DECLARE EXTERNAL  FUNCTION cutoff
   FOR ki=0 TO 20
      FOR kj=0 TO 20
         LET dd = SQR(molecData(ki,1)*molecData(kj,1))
         LET aa = 0.5*(molecData(ki,2)+molecData(kj,2))
         LET r0 = 0.5*(molecData(ki,3)+molecData(kj,3))
         FOR ir=10 TO 1001
            LET r = ir*hh
            LET y = EXP(-aa*(r-r0))
            LET forceTable(ki,kj,ir) = cutoff(r)*2.0*dd*aa*y*(y-1)
         NEXT ir
         FOR ir=0 TO 9
            LET forceTable(ki,kj,ir) = forceTable(ki,kj,10)
         NEXT ir
      NEXT kj
   NEXT ki
END SUB

EXTERNAL FUNCTION cutoff(r)
   IF r>0 AND r<0.8*rCutoff THEN
      LET ret = 1
   ELSEIF r>=0.8*rCutoff AND r<rCutoff THEN
      LET ret = 0.5+0.5*COS(PI*(r-0.8*rCutoff)/(0.2*rCutoff))
   else
      LET ret = 0
   END IF
   LET cutoff = ret
END FUNCTION

! ---------- move particles

EXTERNAL SUB moveParticles(tempMode,contTemp) !tempMode 0:adiabatic  1:constant-temp
   DECLARE EXTERNAL SUB moveParticlesDT,ajustVelocity,registerNearMolec
   IF (tempMode=1) THEN CALL ajustVelocity(contTemp)
   CALL registerNearMolec
   FOR i=1 TO 20
      CALL moveParticlesDT
   NEXT i
END SUB

EXTERNAL SUB moveParticlesDT ! velocity Verlet method
   DECLARE EXTERNAL SUB calcForce
   FOR i=1 TO nMolec
      LET a = 0.5*dt/mas(i)
      LET vx(i) = vx(i)+a*ffx(i)
      LET vy(i) = vy(i)+a*ffy(i)
      LET xx(i) = xx(i)+vx(i)*dt
      LET yy(i) = yy(i)+vy(i)*dt
   NEXT i
   CALL calcForce
   FOR i=1 TO nMolec
      LET a = 0.5*dt/mas(i)
      LET vx(i) = vx(i)+a*ffx(i)
      LET vy(i) = vy(i)+a*ffy(i)
   NEXT i
   LET sysTime=sysTime+dt
END SUB

EXTERNAL SUB calcForce
   DECLARE EXTERNAL FUNCTION force,boundaryForce
   LET s = 0.5*3.418e-10
   FOR i=1 TO nMolec
      LET ffx(i) = 0.0
      LET ffy(i) = 0.0
   NEXT i
   FOR i=1 TO nMolec-1
      FOR k=1 TO reg(i,0)-1
         LET j = reg(i,k)
         LET xij = xx(i)-xx(j)
         LET yij = yy(i)-yy(j)
         LET rij = SQR(xij*xij+yij*yij)
         IF rij<rCutoff THEN
            LET f = force(rij,kind(i),kind(j))
            LET fxij = f*xij/rij
            LET fyij = f*yij/rij
            LET ffx(i) = ffx(i)+fxij
            LET ffy(i) = ffy(i)+fyij
            LET ffx(j) = ffx(j)-fxij
            LET ffy(j) = ffy(j)-fyij
         END IF
      NEXT k
   NEXT i
   FOR i=1 TO nMolec  ! boundary force
      LET ffx(i) = ffx(i)+boundaryForce(xx(i)+s)+boundaryForce(xx(i)-xMax-s)
      LET ffy(i) = ffy(i)+boundaryForce(yy(i)+s)+boundaryForce(yy(i)-yMax-s)
   NEXT i
END SUB

EXTERNAL FUNCTION force(r,ki,kj) !force(r) <-- forceTable - linear interporation
   LET ir = INT(r/hh)
   LET a = r - ir*hh
   LET force = ((hh-a)*forceTable(ki,kj,ir) + a*forceTable(ki,kj,ir+1))/hh
END FUNCTION

EXTERNAL FUNCTION boundaryForce(r)
   LET r6 = (3.418e-10/r)^6
   LET boundaryForce = (24.0*(0.5*1.711e-21)*r6*(2.0*r6-1.0)/r)
END FUNCTION

EXTERNAL SUB registerNearMolec
   LET rCut = rCutoff+20*2000*dt
   LET rcut2 = rCut*rCut
   FOR i=1 TO nMolec-1
      LET k = 1
      FOR j=i+1 TO nMolec
         LET r2 = (xx(i)-xx(j))*(xx(i)-xx(j))+(yy(i)-yy(j))*(yy(i)-yy(j))
         IF (r2<rcut2) THEN
            LET reg(i,k) = j
            LET k = k + 1
         END IF
      NEXT j
      LET reg(i,0) = k
   NEXT i
END SUB

EXTERNAL FUNCTION maxNearMolec
   LET mx = 0
   FOR i=1 TO nMolec-1
      IF mx<reg(i,0) THEN LET mx = reg(i,0)
   NEXT i
   LET maxNearMolec = mx-1
END FUNCTION

! ---------- utility

EXTERNAL FUNCTION systemTemprature
   LET kB = 1.38e-23 ! Boltzman's constant (J/K)
   LET ek= 0.0       !kinetic energy (J)
   FOR i=1 TO nMolec
      LET ek = ek + 0.5*mas(i)*(vx(i)^2+vy(i)^2)
   NEXT i
   LET systemTemprature = ek/(nMolec*kB) !2D: E/N=kT, 3D: E/N=(3/2)kT
END FUNCTION

EXTERNAL SUB ajustVelocity(temp)
   DECLARE EXTERNAL FUNCTION systemTemprature
   LET r = sqr(temp/systemTemprature)
   FOR i=1 TO nMolec
      LET vx(i) = r*vx(i)
      LET vy(i) = r*vy(i)
   NEXT i
END SUB

! ---------- draw particles

EXTERNAL SUB drawParticles(tempMode,contTemp,drawMode)
   DECLARE EXTERNAL FUNCTION systemTemprature,maxNearMolec
   DECLARE EXTERNAL sub realSpace,velocitySpace,plotBond
   SET DRAW MODE HIDDEN
   CLEAR
   IF drawMode=0 OR drawMode=1 THEN !--- 0:circle  1:circle+bond
      call plotBond(drawMode)
   ELSEIF drawMode=2 THEN
      call velocitySpace
   END IF
   !--- draw caption
   SET TEXT HEIGHT 10
   SET TEXT COLOR 1 ! black
   LET tmp$ = "adiabatic   constantTemp  "
   PLOT TEXT, AT  50, 70 ,USING "time =#####.## (ps)   temp =####.## (K)":sysTime*1E12,systemTemprature
   PLOT TEXT, AT  50, 55 ,USING molecSTR$(molecKind1)&","&molecSTR$(molecKind2)&"  N =####":nMolec
   PLOT TEXT, AT  50, 40 ,USING "tempMode = ## ":tempMode
   PLOT TEXT, AT 200, 40 :tmp$(tempMode*12+1:tempMode*12+12)
   PLOT TEXT, AT  50, 25 ,USING "controled Temperature =####.# (K)":contTemp
   PLOT TEXT, AT  50, 10 :"2-dimensional molecular dynamics"
   PLOT TEXT, AT  50,480 :"[esc] exit    [0] temp > value "
   PLOT TEXT, AT  50,460 :"[D] dispMode  [9] menu > select"
   SET DRAW MODE EXPLICIT
END SUB

EXTERNAL sub plotBond(drawMode)
   LET boxSize = 300
   LET mag = boxSize/xMax
   LET xp = 100
   LET yp = 100
   SET LINE COLOR 1 ! black : !--- box
   PLOT LINES: xp,yp; boxSize+xp,yp; boxSize+xp,boxSize+yp; xp,boxSize+yp; xp,yp
   SET TEXT HEIGHT 6
   SET TEXT COLOR 1 ! black
   PLOT TEXT, AT xp,boxSize+2+yp ,USING  "box size =##.# x ##.# (nm)":xMax*1e9,yMax*1e9
   FOR i=1 TO nMolec
      IF kind(i)=molecKind1 THEN SET LINE COLOR 11 ELSE SET LINE COLOR 12
      DRAW circle WITH SCALE(molecData(kind(i),3)/2.0*mag)*SHIFT(xx(i)*mag+xp,yy(i)*mag+yp)
   NEXT i
   IF drawMode=1 THEN
      FOR i=1 TO nMolec-1
         FOR k=1 TO reg(i,0)-1
            LET j = reg(i,k)
            LET r = SQR((xx(i)-xx(j))*(xx(i)-xx(j))+(yy(i)-yy(j))*(yy(i)-yy(j)))
            LET r0 = 0.5*(molecData(kind(i),3)+molecData(kind(j),3))
            IF r<1.2*r0 THEN
               LET yij = yy(i)-yy(j)
               IF yij=0.0 THEN LET yij = 1e-20
               LET th = 3.0*(ATN((xx(i)-xx(j))/yij)+PI/2.0)/PI
               LET col = 240 + INT((th-INT(th))*6)
               SET LINE COLOR col
               PLOT LINES: xx(i)*mag+xp,yy(i)*mag+yp;xx(j)*mag+xp,yy(j)*mag+yp
            END IF
         NEXT k
      NEXT i
   END IF
END sub

EXTERNAL sub velocitySpace
   LET boxSize = 300
   LET xp = 100
   LET yp = 100
   SET LINE COLOR 1 !black : axis
   PLOT LINES: xp,boxSize/2+yp; boxSize+xp,boxSize/2+yp !vx-axis
   PLOT LINES: boxSize/2+xp,yp; boxSize/2+xp,boxSize+yp !vy-axis
   SET TEXT HEIGHT 6
   SET TEXT COLOR 1 ! black
   PLOT TEXT, AT boxSize+xp,boxSize/2+yp: "vx"
   PLOT TEXT, AT boxSize+xp,boxSize/2-12+yp: "2000m/s"
   PLOT TEXT, AT boxSize/2-12+xp,boxSize+yp: "vy  2000m/s"
   PLOT TEXT, AT boxSize/2-8+xp,boxSize/2-10+yp: "0"
   PLOT TEXT, AT xp,boxSize+8+yp: "velocity space (vx,vy)"
   LET mag = boxSize/4000
   FOR i=1 TO nMolec
      IF kind(i)=molecKind1 THEN SET LINE COLOR 11 ELSE SET LINE COLOR 12
      DRAW circle WITH SCALE(5)*SHIFT(vx(i)*mag+boxSize/2+xp,vy(i)*mag+boxSize/2+yp)
   NEXT i
END sub
END MODULE
 

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