Source Code for Module reflectometry.model3d.par_structure

  1  # Copyright (C) 2008 University of Maryland 
  2  # All rights reserved. 
  3  # See LICENSE.txt for details. 
  4  # Author: Christopher Metting 
  5  # Starting Date: 4/14/2008 
  6   
  7  ''' 
  8  Structure class and function for operating on it 
  9   
 10  Treats the ordering of features along a two dimentional rectilinear lattice 
 11  structure with the born approximation providing the scattering resulting from 
 12  a rectilinear lattice of particles on a substrate 
 13   
 14  ''' 
 15   
 16   
 17  from numpy import shape,ones,sin,empty 
 18 -class Rectilinear(object): 
 19      ''' 
 20      This contains variables to define the sample rectilinear lattice 
 21   
 22      Dx,Dy (Angstrom) 
 23          width,length of a single unit cell 
 24      nx,ny (integer) 
 25          number of repeat unit cells in x,y direction 
 26   
 27      ''' 
 28 -    def __init__(self,Dx = None,Dy = None,nx = 50, ny = None): 
 29          ''' 
 30          Dy defaults to Dx 
 31          ny defaults to nx 
 32          ''' 
 33          self.Dx = Dx 
 34          self.Dy = Dy if Dy is not None else Dx 
 35          self.nx = nx 
 36          self.ny = ny if ny is not None else nx 
 37   
 38 -    def eval(self,qx,qy,qz): 
 39   
 40          RIFz = ones(qz.shape); 
 41          RIFxyz = empty([len(qx),len(qy),len(qz)],'d') # Complex 'D' real 'd' 
 42   
 43          for i,qxi in enumerate(qx): 
 44              for j,qyj in enumerate(qy): 
 45   
 46                  #%Chucks first formula component without the y values 
 47                  RIFxi = par_lattice(qxi,self.Dx,self.nx) 
 48                  RIFyj = par_lattice(qyj,self.Dy,self.ny) 
 49                  RIFxz = RIFxi * RIFz 
 50                  RIFxyz[i,j,:] = RIFxz * RIFyj 
 51   
 52          return RIFxyz 
 53   
 54 -def structure_loop(qx,qy,qz,struc): 
 55   
 56      RIFz = ones(qz.shape); 
 57      RIFxyz = empty([len(qx),len(qy),len(qz)],'d') # Complex 'D' real 'd' 
 58   
 59      for i,qxi in enumerate(qx): 
 60          for j,qyj in enumerate(qy): 
 61   
 62              #%Chucks first formula component without the y values 
 63              RIFxi = par_lattice(qxi,struc.Dx,struc.nx) 
 64              RIFyj = par_lattice(qyj,struc.Dy,struc.ny) 
 65              RIFxz = RIFxi * RIFz 
 66              RIFxyz[i,j,:] = RIFxz * RIFyj 
 67   
 68      return RIFxyz 
 69   
 70 -def par_lattice(q,lattice_param,domain): 
 71      """ 
 72      Attempts to Calculate the Structure Factor of the sin portion of chucks 
 73      equations. 
 74      """ 
 75   
 76      if q == 0: 
 77          RIF =  domain**2 
 78      else: 
 79          RIF = (sin((q*lattice_param*domain)/2)) / (sin((q*lattice_param)/2)) 
 80   
 81      return RIF 
 82   
 83   
 84   
 85   
 86 -def test(): 
 87      from numpy import array 
 88      s = Rectilinear(nx = 12) 
 89      assert s.ny == 12, "expected ny = nx" 
 90   
 91      lattice = Rectilinear(Dx = 3, nx = 2) 
 92      qx,qy,qz = array([1]),array([1]),array([1]) 
 93      v = structure_loop(qx,qy,qz,lattice) 
 94      v = lattice.eval(qx,qy,qz) 
 95   
 96      c = (sin((1*3*2)/2)) / (sin((1*3)/2)) 
 97      assert abs(v - c**2)< 1e-15, "expected %g but got %g" %(v,c**2) 
 98  if __name__ == "__main__": 
 99      test() 
100