Calculate PDF from a 2D slab with analytic baseline

NaCl.cif

#------------------------------------------------------------------------------
#$Date: 2010-01-30 13:59:17 +0000 (Sat, 30 Jan 2010) $
#$Revision: 966 $
#$URL: svn://cod.ibt.lt/cod/cif/1/1000041.cif $
#------------------------------------------------------------------------------
#
# This file is available in the Crystallography Open Database (COD),
# http://www.crystallography.net/
#
# All data on this site have been placed in the public domain by the
# contributors.
#
data_1000041

_chemical_name_systematic          'Sodium chloride'
_chemical_formula_structural       'Na Cl'
_chemical_formula_sum              'Cl Na'

_publ_section_title
;
Accuracy of an automatic diffractometer. measurement of the sodium
chloride structure factors
;
loop_
_publ_author_name
  'Abrahams, S C'
  'Bernstein, J L'
_journal_name_full                 'Acta Crystallographica (1,1948-23,1967)'
_journal_coden_ASTM                ACCRA9
_journal_volume                    18
_journal_year                      1965
_journal_page_first                926
_journal_page_last                 932

_cell_length_a                     5.62
_cell_length_b                     5.62
_cell_length_c                     5.62
_cell_angle_alpha                  90
_cell_angle_beta                   90
_cell_angle_gamma                  90
_cell_volume                       177.5
_cell_formula_units_Z              4

_symmetry_space_group_name_H-M     'F m -3 m'
_symmetry_Int_Tables_number        225
_symmetry_cell_setting             cubic

loop_
_symmetry_equiv_pos_as_xyz
  'x,y,z'
  'y,z,x'
  'z,x,y'
  'x,z,y'
  'y,x,z'
  'z,y,x'
  'x,-y,-z'
  'y,-z,-x'
  'z,-x,-y'
  'x,-z,-y'
  'y,-x,-z'
  'z,-y,-x'
  '-x,y,-z'
  '-y,z,-x'
  '-z,x,-y'
  '-x,z,-y'
  '-y,x,-z'
  '-z,y,-x'
  '-x,-y,z'
  '-y,-z,x'
  '-z,-x,y'
  '-x,-z,y'
  '-y,-x,z'
  '-z,-y,x'
  '-x,-y,-z'
  '-y,-z,-x'
  '-z,-x,-y'
  '-x,-z,-y'
  '-y,-x,-z'
  '-z,-y,-x'
  '-x,y,z'
  '-y,z,x'
  '-z,x,y'
  '-x,z,y'
  '-y,x,z'
  '-z,y,x'
  'x,-y,z'
  'y,-z,x'
  'z,-x,y'
  'x,-z,y'
  'y,-x,z'
  'z,-y,x'
  'x,y,-z'
  'y,z,-x'
  'z,x,-y'
  'x,z,-y'
  'y,x,-z'
  'z,y,-x'
  'x,1/2+y,1/2+z'
  '1/2+x,y,1/2+z'
  '1/2+x,1/2+y,z'
  'y,1/2+z,1/2+x'
  '1/2+y,z,1/2+x'
  '1/2+y,1/2+z,x'
  'z,1/2+x,1/2+y'
  '1/2+z,x,1/2+y'
  '1/2+z,1/2+x,y'
  'x,1/2+z,1/2+y'
  '1/2+x,z,1/2+y'
  '1/2+x,1/2+z,y'
  'y,1/2+x,1/2+z'
  '1/2+y,x,1/2+z'
  '1/2+y,1/2+x,z'
  'z,1/2+y,1/2+x'
  '1/2+z,y,1/2+x'
  '1/2+z,1/2+y,x'
  'x,1/2-y,1/2-z'
  '1/2+x,-y,1/2-z'
  '1/2+x,1/2-y,-z'
  'y,1/2-z,1/2-x'
  '1/2+y,-z,1/2-x'
  '1/2+y,1/2-z,-x'
  'z,1/2-x,1/2-y'
  '1/2+z,-x,1/2-y'
  '1/2+z,1/2-x,-y'
  'x,1/2-z,1/2-y'
  '1/2+x,-z,1/2-y'
  '1/2+x,1/2-z,-y'
  'y,1/2-x,1/2-z'
  '1/2+y,-x,1/2-z'
  '1/2+y,1/2-x,-z'
  'z,1/2-y,1/2-x'
  '1/2+z,-y,1/2-x'
  '1/2+z,1/2-y,-x'
  '-x,1/2+y,1/2-z'
  '1/2-x,y,1/2-z'
  '1/2-x,1/2+y,-z'
  '-y,1/2+z,1/2-x'
  '1/2-y,z,1/2-x'
  '1/2-y,1/2+z,-x'
  '-z,1/2+x,1/2-y'
  '1/2-z,x,1/2-y'
  '1/2-z,1/2+x,-y'
  '-x,1/2+z,1/2-y'
  '1/2-x,z,1/2-y'
  '1/2-x,1/2+z,-y'
  '-y,1/2+x,1/2-z'
  '1/2-y,x,1/2-z'
  '1/2-y,1/2+x,-z'
  '-z,1/2+y,1/2-x'
  '1/2-z,y,1/2-x'
  '1/2-z,1/2+y,-x'
  '-x,1/2-y,1/2+z'
  '1/2-x,-y,1/2+z'
  '1/2-x,1/2-y,z'
  '-y,1/2-z,1/2+x'
  '1/2-y,-z,1/2+x'
  '1/2-y,1/2-z,x'
  '-z,1/2-x,1/2+y'
  '1/2-z,-x,1/2+y'
  '1/2-z,1/2-x,y'
  '-x,1/2-z,1/2+y'
  '1/2-x,-z,1/2+y'
  '1/2-x,1/2-z,y'
  '-y,1/2-x,1/2+z'
  '1/2-y,-x,1/2+z'
  '1/2-y,1/2-x,z'
  '-z,1/2-y,1/2+x'
  '1/2-z,-y,1/2+x'
  '1/2-z,1/2-y,x'
  '-x,1/2-y,1/2-z'
  '1/2-x,-y,1/2-z'
  '1/2-x,1/2-y,-z'
  '-y,1/2-z,1/2-x'
  '1/2-y,-z,1/2-x'
  '1/2-y,1/2-z,-x'
  '-z,1/2-x,1/2-y'
  '1/2-z,-x,1/2-y'
  '1/2-z,1/2-x,-y'
  '-x,1/2-z,1/2-y'
  '1/2-x,-z,1/2-y'
  '1/2-x,1/2-z,-y'
  '-y,1/2-x,1/2-z'
  '1/2-y,-x,1/2-z'
  '1/2-y,1/2-x,-z'
  '-z,1/2-y,1/2-x'
  '1/2-z,-y,1/2-x'
  '1/2-z,1/2-y,-x'
  '-x,1/2+y,1/2+z'
  '1/2-x,y,1/2+z'
  '1/2-x,1/2+y,z'
  '-y,1/2+z,1/2+x'
  '1/2-y,z,1/2+x'
  '1/2-y,1/2+z,x'
  '-z,1/2+x,1/2+y'
  '1/2-z,x,1/2+y'
  '1/2-z,1/2+x,y'
  '-x,1/2+z,1/2+y'
  '1/2-x,z,1/2+y'
  '1/2-x,1/2+z,y'
  '-y,1/2+x,1/2+z'
  '1/2-y,x,1/2+z'
  '1/2-y,1/2+x,z'
  '-z,1/2+y,1/2+x'
  '1/2-z,y,1/2+x'
  '1/2-z,1/2+y,x'
  'x,1/2-y,1/2+z'
  '1/2+x,-y,1/2+z'
  '1/2+x,1/2-y,z'
  'y,1/2-z,1/2+x'
  '1/2+y,-z,1/2+x'
  '1/2+y,1/2-z,x'
  'z,1/2-x,1/2+y'
  '1/2+z,-x,1/2+y'
  '1/2+z,1/2-x,y'
  'x,1/2-z,1/2+y'
  '1/2+x,-z,1/2+y'
  '1/2+x,1/2-z,y'
  'y,1/2-x,1/2+z'
  '1/2+y,-x,1/2+z'
  '1/2+y,1/2-x,z'
  'z,1/2-y,1/2+x'
  '1/2+z,-y,1/2+x'
  '1/2+z,1/2-y,x'
  'x,1/2+y,1/2-z'
  '1/2+x,y,1/2-z'
  '1/2+x,1/2+y,-z'
  'y,1/2+z,1/2-x'
  '1/2+y,z,1/2-x'
  '1/2+y,1/2+z,-x'
  'z,1/2+x,1/2-y'
  '1/2+z,x,1/2-y'
  '1/2+z,1/2+x,-y'
  'x,1/2+z,1/2-y'
  '1/2+x,z,1/2-y'
  '1/2+x,1/2+z,-y'
  'y,1/2+x,1/2-z'
  '1/2+y,x,1/2-z'
  '1/2+y,1/2+x,-z'
  'z,1/2+y,1/2-x'
  '1/2+z,y,1/2-x'
  '1/2+z,1/2+y,-x'

loop_
_atom_type_symbol
_atom_type_oxidation_number
  Na1+   1.000
  Cl1-  -1.000

loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_symmetry_multiplicity
_atom_site_Wyckoff_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
_atom_site_attached_hydrogens
_atom_site_calc_flag
  Na1   Na1+   4 a 0. 0. 0. 1.  0 d
  Cl1   Cl1-   4 b 0.5 0.5 0.5 1.  0 d

_refine_ls_R_factor_all            0.022



_cod_database_code 1000041

slabpdfdemo.py

import numpy
import copy
from diffpy.Structure import loadStructure, Lattice
from diffpy.srreal.pdfcalculator import PDFCalculator, DebyePDFCalculator
from diffpy.srreal.pdfbaseline import makePDFBaseline, PDFBaseline
from matplotlib.pyplot import *

# load bulk crystal structure
nacl = loadStructure('NaCl.cif')
nacl.Uisoequiv = 0.004
numdensity = len(nacl) / nacl.lattice.volume
cell_height = nacl.lattice.c

# Convert bulk structure to a slab with a thickness
# of the lattice parameter c.  We do this by assuming
# new unit cell with parameter c much larger than the
# PDF range.
nacl_slab = copy.copy(nacl)
slab_lattice = copy.copy(nacl.lattice)
slab_lattice.c = 200
# this adjusts fractional coordinates so that atom
# separation along c remain the same.
nacl_slab.placeInLattice(slab_lattice)


# analytic shape function for an infinite slab of thickness t
def slab_shape_function(r, thickness):
    x = numpy.asarray(r, dtype=float).reshape(-1)
    fshape = numpy.zeros_like(r)
    lo = x < thickness
    hi = ~lo
    fshape[lo] = 1 - 0.5 * x[lo] / thickness
    fshape[hi] = + 0.5 * thickness / x[hi]
    if numpy.isscalar(r):
        fshape = numpy.asscalar(fshape)
    return fshape


# PDF baseline due to the sample shape:
def slab_pdf_baseline(r, thickness):
    ybase = -4 * numpy.pi * r * numdensity * slab_shape_function(r, thickness)
    return ybase


# makePDFBaseline allows to use the new baseline function with PDFCalculator.
# Cover your eyes - it only works once per Python session.  Do nothing if
# already done.
if not 'slab_baseline' in PDFBaseline.getRegisteredTypes():
    makePDFBaseline('slab_baseline',
            slab_pdf_baseline, thickness=cell_height)


# standard real-space PDF calculator
pdfc = PDFCalculator(rmax=40, qmax=25)
# real-space PDF calculator setup to use slab baseline function
pdfcslab = pdfc.copy()
pdfcslab.baseline = 'slab_baseline'
# PDF calculator using Debye summation and an intensity cutoff below qmin
dbpdfc = DebyePDFCalculator(rmax=40, qmax=25, qmin=1)

# plot it
clf()
a1 = subplot(2, 1, 1)
a1.plot(*pdfc(nacl))
a1.plot(*pdfc(nacl_slab))
a1.set_title('Bulk and slab PDF with standard baseline')
a2 = subplot(2, 1, 2)
a2.plot(*pdfcslab(nacl_slab))
a2.plot(*dbpdfc(nacl_slab))
a2.set_title('PDF with analytic slab baseline and PDF from Debye summation')
show()