fourier¶

This module define the Fourier class and other functions related to the fourier transformation.

class javelin.fourier.Fourier[source]¶

The Fourier class contains everything required to calculate the diffuse scattering. The only required thing to be set is javelin.fourier.Fourier.structure. There are defaults for all other options including grid, radiation, average structure subtraction and lots options.

Examples:

>>> from javelin.structure import Structure
>>> fourier = Fourier()
>>> print(fourier)
Radiation         : neutron
Fourier volume    : complete crystal
Aver. subtraction : False
<BLANKLINE>
Reciprocal layer  :
lower left  corner :     [ 0.  0.  0.]
lower right corner :     [ 1.  0.  0.]
upper left  corner :     [ 0.  1.  0.]
top   left  corner :     [ 0.  0.  1.]
<BLANKLINE>
hor. increment     :     [ 0.01  0.    0.  ]
vert. increment    :     [ 0.    0.01  0.  ]
top   increment    :     [ 0.  0.  1.]
<BLANKLINE>
# of points        :     101 x 101 x 1
>>> results = fourier.calc(Structure())
>>> print(results) # doctest: +SKIP
<xarray.DataArray 'Intensity' ([ 1.  0.  0.]: 101, [ 0.  1.  0.]: 101, [ 0.  0.  1.]: 1)>
array([[[ 0.],
        [ 0.],
        ...,
        [ 0.],
        [ 0.]],
<BLANKLINE>
       [[ 0.],
        [ 0.],
        ...,
        [ 0.],
        [ 0.]],
<BLANKLINE>
       ...,
       [[ 0.],
        [ 0.],
        ...,
        [ 0.],
        [ 0.]],
<BLANKLINE>
       [[ 0.],
        [ 0.],
        ...,
        [ 0.],
        [ 0.]]])
Coordinates:
  * [ 1.  0.  0.]  ([ 1.  0.  0.]) float64 0.0 0.01 0.02 0.03 0.04 0.05 0.06 ...
  * [ 0.  1.  0.]  ([ 0.  1.  0.]) float64 0.0 0.01 0.02 0.03 0.04 0.05 0.06 ...
  * [ 0.  0.  1.]  ([ 0.  0.  1.]) float64 0.0
Attributes:
    units:    r.l.u

approximate¶

This sets the options of calculating the approximate scattering instead of exact. This is much quicker and is likely good enough for most cases.

Getter:	Returns bool of approximate scattering option
Setter:	Sets whether approximate sacttering is calculated
Type:	bool

average¶

This sets the options of calculating average structure and subtracted it from the simulated scattering

Getter:	Returns bool of average structure subtraction option
Setter:	Sets whether average structure is subtracted
Type:	bool

calc(structure)[source]¶

Calculates the fourier transform

Parameters:	structure – The structure from which fourier transform

is calculated. The calculation work with any of the following types of structures javelin.structure.Structure, ase.Atoms or diffpy.Structure.structure.Structure but if you are using average structure subtraction or the lots option it needs to be javelin.structure.Structure type.

Returns:	DataArray containing calculated diffuse scattering
Return type:	`xarray.DataArray`

calc_average(structure)[source]¶

Calculates the scattering from the avarage structure

Parameters:	structure – The structure from which fourier transform

is calculated. The calculation work with any of the following types of structures javelin.structure.Structure, ase.Atoms or diffpy.Structure.structure.Structure but if you are using average structure subtraction or the lots option it needs to be javelin.structure.Structure type.

Returns:	DataArray containing calculated average scattering
Return type:	`xarray.DataArray`

grid = None¶: The grid attribute defines the reciprocal volume from which the scattering will be calculated. Must of type javelin.grid.Grid And check javelin.grid.Grid for details on how to change the grid.

lots¶

The size of lots

Getter:	Returns the lots size
Setter:	Sets the lots size
Type:	list of 3 integers or None

magnetic¶

This sets the options of calculating the magnetic scattering instead of nuclear. This assume neutrons are being used.

Getter:	Returns bool of magnetic scattering option
Setter:	Sets whether magnetic sacttering is calculated
Type:	bool

number_of_lots¶

The number of lots to use

Getter:	Returns the number of lots
Setter:	Sets the number of lots
Type:	int

radiation¶

The radiation used

Getter:	Returns the radiation selected
Setter:	Sets the radiation
Type:	str (‘xray’ or ‘neutron’)

javelin.fourier.create_xarray_dataarray(values, grid)[source]¶

Create a xarry DataArray from the input numpy array and grid object.

Parameters:	values (`numpy.ndarray`) – Input array containing the scattering intensities numbers (`javelin.grid.Grid`) – Grid object describing the array properties
Returns:	DataArray produced from the values and grid object
Return type:	`xarray.DataArray`

javelin.fourier.get_ff(atomic_number, radiation, q=None)[source]¶

Returns the form factor for a given atomic number, radiation and q values

Parameters:	atomic_number (int) – atomic number radiation (str) – type of radiation (‘xray’ or ‘neutron’) q (float, list, `numpy.ndarray`) – value or values of q for which to get form factors
Returns:	form factors for given q
Return type:	float, `numpy.ndarray`
Examples:

>>> get_ff(8, 'neutron')
5.805

>>> get_ff(8, 'xray', q=2.0)
6.31826029176493

>>> get_ff(8, 'xray', q=[0.0, 3.5, 7.0])
array([ 7.999706  ,  4.38417867,  2.08928068])

javelin.fourier.get_mag_ff(atomic_number, q, ion=0, j=0)[source]¶

Returns the j0 magnetic form factor for a given atomic number, radiation and q values

Parameters:	atomic_number (int) – atomic number q (float, list, `numpy.ndarray`) – value or values of q for which to get form factors ion (int) – charge of selected atom j (int) – order of spherical Bessel function (0, 2, 4 or 6)
Returns:	magnetic form factor for given q
Return type:	float, `numpy.ndarray`
Examples:

>>> get_mag_ff(8, q=2, ion=1)
0.58510426376585045

>>> get_mag_ff(26, q=[0.0, 3.5, 7.0], ion=2)
array([ 1.        ,  0.49729671,  0.09979243])

>>> get_mag_ff(26, q=[0.0, 3.5, 7.0], ion=4)
array([ 0.9997    ,  0.58273549,  0.13948496])

>>> get_mag_ff(26, q=[0.0, 3.5, 7.0], ion=4, j=4)
array([ 0.       ,  0.0149604,  0.0759222])