Class: Aims::ZincBlende

Inherits:
Object
  • Object
show all
Includes:
Vectorize, Math
Defined in:
lib/aims/zinc_blende.rb

Overview

Factory class for generating slabs for various crystal surfaces of specified thickness and with the specified vacuum. Example:

zb = ZincBlende.new("Ga", "As", 5.65)
zb.get_bulk -> # returns the a unit cell with two atoms
zb.get_111B_surface(7, 20, 3) # returns a slab of 111B 7 monolayers thick, with 20 angstrom of vacuum, and the bottom 3 layers constrained

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods included from Vectorize

#cross, #dot

Constructor Details

#initialize(cation, anion, lattice_const) ⇒ ZincBlende

Initialize the zinc-blende Geometry cation and anion are the atomic species occupying the two different sub-lattices. lattice_const specifies the lattice constant



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# File 'lib/aims/zinc_blende.rb', line 22

def initialize(cation, anion, lattice_const)
  self.lattice_const = lattice_const
  self.cation = cation
  self.anion = anion
end

Instance Attribute Details

#anion ⇒ Object

Returns the value of attribute anion.



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# File 'lib/aims/zinc_blende.rb', line 16

def anion
  @anion
end

#cation ⇒ Object

Returns the value of attribute cation.



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# File 'lib/aims/zinc_blende.rb', line 16

def cation
  @cation
end

#lattice_const ⇒ Object

Returns the value of attribute lattice_const.



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# File 'lib/aims/zinc_blende.rb', line 16

def lattice_const
  @lattice_const
end

Instance Method Details

#fill_volume(volume) ⇒ Object

Fill the given volume with atoms



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# File 'lib/aims/zinc_blende.rb', line 49

def fill_volume(volume)
  
  # First fill a cube that bounds the volume
  max = volume.max_point
  min = volume.min_point
  
  dx = max[0] - min[0]
  dy = max[1] - min[1]
  dz = max[2] - min[2]
  
  bulk = get_bulk
  
  # This inverse matrix gives the number of repetitions 
  m = Matrix[[dx,0,0], [0,dy,0], [0,0,dz]]
  v = Matrix[bulk.lattice_vectors[0].to_a, 
             bulk.lattice_vectors[1].to_a,
             bulk.lattice_vectors[2].to_a]
  rep_mat = m*(v.inverse)
  
  # The only way I can figure out how to do this for an 
  # arbitrary set of lattice vectors is to fill the volume
  # out along each edge of the super-cube and then eliminate duplicates
  atoms = []
  3.times do |i|
    # this vector is the number of repetitions in the unit cell
    # to fill the volume out along the i-th edge of the super-cube
    n_repeat = rep_mat.row(i)
    
    # Give the proper sign to the repeat
    nx = (n_repeat[0] < 0) ? n_repeat[0].floor-1 : n_repeat[0].ceil+1
    ny = (n_repeat[1] < 0) ? n_repeat[1].floor-1 : n_repeat[1].ceil+1
    nz = (n_repeat[2] < 0) ? n_repeat[2].floor-1 : n_repeat[2].ceil+1
    
    atoms += bulk.repeat(nx, ny, nz).atoms.find_all{|a| volume.contains_point(a.x, a.y, a.z)}
  end
  Geometry.new(atoms.uniq)
end

#get_001_surface(monolayers, vacuum, constrain_layers = 0) ⇒ Object Also known as: get_100_surface, get_010_surface

Return a unit cell for a slab of 001 Specify the number of atomic monolayers, the vacuum thickness in angstrom, and the number of layers to constrain at the base of the slab



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# File 'lib/aims/zinc_blende.rb', line 91

def get_001_surface(monolayers, vacuum, constrain_layers = 0)
  anion = Atom.new(0,0,0,self.cation)
  cation = Atom.new(0.25*self.lattice_const, 0.25*self.lattice_const, 0.25*self.lattice_const, self.anion)
  v1 = Vector[0.5, 0.5, 0]*self.lattice_const
  v2 = Vector[-0.5,0.5,0]*self.lattice_const
  v3 = Vector[0.5, 0, 0.5]*self.lattice_const
  
  zb = Geometry.new([anion, cation], [v1,v2,v3])
  millerX = [1,0,0]
  millerY = [0,1,0]
  millerZ = [0,0,1]
  zb.set_miller_indices(millerX, millerY, millerZ)
  
  # Repeat the unit cell.  The unit cell is a bi-layer so divide by 2
  zb = zb.repeat(1,1,(monolayers/2).ceil)

  if 0 < vacuum
    # Add vacuum
    monolayerSep = v3[2]/2
    zb.lattice_vectors[2] = Vector[0, 0, (monolayers-1)*monolayerSep.abs + vacuum.to_f]
    # Move everything into a nice tidy unit cell. 
    zb = zb.correct
  end

  minZ = zb.atoms.min{|a,b| a.z <=> b.z}.z
  
  # Reject the top layer of atoms if an odd number of monolayers was requested.
  # This is necessary because the primitive cell is a bilayer
  zb.atoms.reject! {|a| 
    a.z >= (minZ + monolayerSep.abs*monolayers)
  }
  
  # Constrain the bottom layers
  zb.atoms.each{|a|
    if (a.z < minZ + monolayerSep.abs*constrain_layers)
      a.constrain = ".true."
    end
  }
  
  # Return the completed unit cell
  return zb
end

#get_110_surface(monolayers, vacuum = 0, constrain_layers = 0) ⇒ Object

Return a unit cell for a slab of 110 specify the number of atomic monolayers and the vacuum thickness in angstrom



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# File 'lib/aims/zinc_blende.rb', line 266

def get_110_surface(monolayers, vacuum=0, constrain_layers = 0)

  # The atoms on a FCC 
  atom1 = Atom.new(0,0,0,self.cation)
  atom2 = Atom.new(self.lattice_const*1/(2*sqrt(2)), self.lattice_const*0.25, 0.0, self.anion)

  # The lattice Vectors
  v1 = Vector[1/sqrt(2), 0.0, 0.0]*self.lattice_const
  v2 = Vector[0.0, 1.0, 0.0]*self.lattice_const
  v3 = Vector[1/(2*sqrt(2)), -0.5, 1/(2*sqrt(2))]*self.lattice_const

  # The miller indices for each primitive cartesian direction
  millerX = Vector[1, -1, 0]
  millerY = Vector[0, 0, 1]
  millerZ = Vector[1, 1, 0]

  # The unit cell
  zb = Geometry.new([atom1, atom2], [v1, v2, v3])
  zb.set_miller_indices(millerX, millerY, millerZ)

  # Repeat the unit cell
  zb = zb.repeat(1,1,monolayers)


  monolayerSep = v3[2]
  if 0 < vacuum
    # Add vacuum
    zb.lattice_vectors[2] = Vector[0, 0, (monolayers-1)*monolayerSep.abs + vacuum.to_f]
    # Move everything into a nice tidy unit cell. 
    zb = zb.correct
  end

  # # Constrain the bottom layers
  zb.atoms.each{|a|
    if (a.z < monolayerSep*constrain_layers)
      a.constrain = ".true."
    end
  }

  
  # Return the completed unit cell
  return zb
end

#get_111_surface(dir, monolayers, vacuum, constrain_layers = 0) ⇒ Object

Return a unit cell for a slab of 111 dir is either “A” or “B” for the cation or anion terminated slab specify the number of atomic monolayers and the vacuum thickness in angstrom



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# File 'lib/aims/zinc_blende.rb', line 157

def get_111_surface(dir, monolayers, vacuum, constrain_layers = 0)

  if dir == "A"
    top_atom = self.anion
    bot_atom = self.cation
  elsif dir == "B"
    top_atom = self.cation
    bot_atom = self.anion
  else
    raise "Direction must be either A or B"
  end
  
  # The atoms on a FCC 
  as1 = Atom.new(0.0, 0.0, 0.0, top_atom)
  ga1 = Atom.new(0.0, 0.0, -sqrt(3)/4*self.lattice_const, bot_atom)

  # The lattice Vectors
  v1 = Vector[0.5*sqrt(2), 0.0, 0.0]*self.lattice_const
  v2 = Vector[sqrt(2)*0.25, sqrt(6)*0.25, 0.0]*self.lattice_const
  v3 = Vector[sqrt(2)*0.25, sqrt(2.0/3.0)*0.25, -1*sqrt(4.0/3.0)*0.5]*self.lattice_const

  # The unit cell
  zb = Geometry.new([as1, ga1], [v1, v2, v3])

  # The Miller Indices
  millerX = [-1, 1, 0]  # Orientation of the crystal pointing in the cartesian +x axis
  millerY = [1, 1, -2]  # Orientation of the crystal pointing in the cartesian +y axis
  millerZ = [-1, -1, -1] # Orientation of the crystal pointing in the cartesian +z axis

  zb.set_miller_indices(millerX, millerY, millerZ)

  # Repeat the unit cell and add vacuum
  if 0 < vacuum 
    # We actually repeat the unit cell monolayers+1 times because
    # I will strip off the top and bottom atoms to make the proper surface
    zb = zb.repeat(1,1,monolayers+1)
    
    bilayerSep = v3[2]
    zb.lattice_vectors[2] = Vector[0, 0, (monolayers-1)*(bilayerSep.abs) + vacuum]

    # Strip off the top and bottom atom
    minZ = zb.atoms.min{|a,b| a.z <=> b.z}.z
    maxZ = zb.atoms.max{|a,b| a.z <=> b.z}.z

    zb.atoms.reject!{|a| a.z == maxZ}
    zb.atoms.reject!{|a| a.z == minZ}

    # Constrain the bottom layers if requested
    if 0 < constrain_layers
      # get the min again because we removed the atoms at minZ above
      minZ = zb.atoms.min{|a,b| a.z <=> b.z}.z
      constrain_below = minZ + bilayerSep.abs*constrain_layers
      zb.atoms.each{|a|
        if (a.z < constrain_below)
          a.constrain = ".true."
        end
      }
    end
  end
  
  zb
end

#get_111A_surface(monolayers, vacuum, constrain_layers = 0) ⇒ Object

Return a unit cell for a slab of 111A (anion terminated) specify the number of atomic monolayers, the vacuum thickness in angstrom, and the number of layers to constrain at the base of the slab



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# File 'lib/aims/zinc_blende.rb', line 140

def get_111A_surface(monolayers, vacuum, constrain_layers = 0)
  # get the 111B surface, then reflect it about z=0
  get_111_surface("A", monolayers, vacuum, constrain_layers)
end

#get_111B_surface(monolayers, vacuum, constrain_layers = 0) ⇒ Object

Return a unit cell for a slab of 111A (cation terminated) specify the number of atomic monolayers, the vacuum thickness in angstrom, and the number of layers to constrain at the base of the slab



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# File 'lib/aims/zinc_blende.rb', line 149

def get_111B_surface(monolayers, vacuum, constrain_layers = 0)
  get_111_surface("B", monolayers, vacuum, constrain_layers)
end

#get_112_surface(monolayers, vacuum = 0, constrain_layers = 0) ⇒ Object

return a unit cell for a slab of 112 specify the number of atomic monolayers and the vacuum thickness in angstrom



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# File 'lib/aims/zinc_blende.rb', line 222

def get_112_surface(monolayers, vacuum=0, constrain_layers = 0)
  atom1 = Atom.new(0,0,0,self.cation)
  atom2 = Atom.new(self.lattice_const*sqrt(3)/2, 0, 0, self.anion)
  
  v1 = Vector[sqrt(3), 0, 0]*self.lattice_const
  v2 = Vector[0, sqrt(2)/2, 0]*self.lattice_const
  v3 = Vector[1/sqrt(3), 1/(sqrt(3)*2), -1/(sqrt(3)*2)]*self.lattice_const
  
  millerX = Vector[1, 1, -2];
  millerY = Vector[-1, 1, 0];
  millerZ = Vector[-1, -1, -1]

  # The unit cell
   zb = Geometry.new([atom1, atom2], [v1, v2, v3])
   zb.set_miller_indices(millerX, millerY, millerZ)

   # Repeat the unit cell
   zb = zb.repeat(1,1,monolayers)


   if 0 < vacuum
     # Add vacuum
     monolayerSep = v3[2]
     zb.lattice_vectors[2] = Vector[0, 0, (monolayers*monolayerSep).abs + vacuum.to_f]
     # Move everything into a nice tidy unit cell. 
     zb = zb.correct
   end

   # # Constrain the bottom 2 layers
   # zb.atoms.each{|a|
   #   if (a.z < monolayerSep*2)
   #     a.constrain = ".true."
   #   end
   # }


   # Return the completed unit cell
   return zb
end

#get_bulk ⇒ Object

Return the traditional unit cell of bulk zinc blende



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# File 'lib/aims/zinc_blende.rb', line 29

def get_bulk
  b = 0.25*self.lattice_const
  a1 = Atom.new(0, 0, 0, self.cation)
  a2 = Atom.new(b, b, b, self.anion)
  
  v1 = Vector[0.5, 0.5, 0.0]*self.lattice_const
  v2 = Vector[0.5, 0.0, 0.5]*self.lattice_const
  v3 = Vector[0.0, 0.5, 0.5]*self.lattice_const
  zb = Geometry.new([a1, a2], [v1, v2, v3])
  
  millerx = [1, 0, 0]
  millery = [0, 1, 0]
  millerz = [0, 0, 1]
  
  zb.set_miller_indices(millerx, millery, millerz)
  
  return zb
end