#!/usr/bin/env python
##############################################################################
#
# diffpy.morph by DANSE Diffraction group
# Simon J. L. Billinge
# (c) 2010 Trustees of the Columbia University
# in the City of New York. All rights reserved.
#
# File coded by: Chris Farrow
#
# See AUTHORS.txt for a list of people who contributed.
# See LICENSE.txt for license information.
#
##############################################################################
"""Class MorphSphere -- apply a spherical shape function to the morph class
MorphSpheroid -- apply a spheroidal shape function to the morph."""
import numpy
from numpy import arctan as atan
from numpy import arctanh as atanh
from numpy import sqrt
from diffpy.morph.morphs.morph import LABEL_GR, LABEL_RA, Morph
[docs]
class MorphSphere(Morph):
"""Apply a spherical characteristic function to the morph.
Configuration Variables
-----------------------
radius
The radius of the sphere.
"""
# Define input output types
summary = "Apply spherical characteristic function to morph"
xinlabel = LABEL_RA
yinlabel = LABEL_GR
xoutlabel = LABEL_RA
youtlabel = LABEL_GR
parnames = ["radius"]
[docs]
def morph(self, x_morph, y_morph, x_target, y_target):
"""Apply a scale factor."""
Morph.morph(self, x_morph, y_morph, x_target, y_target)
f = _sphericalCF(x_morph, 2 * self.radius)
self.y_morph_out *= f
return self.xyallout
# End of class MorphSphere
[docs]
class MorphSpheroid(Morph):
"""Apply a spherical characteristic function to the morph.
Configuration Variables
-----------------------
radius
The equatorial radius of the spheroid.
pradius
The polar radius of the spheroid.
"""
# Define input output types
summary = "Apply spheroidal characteristic function to morph"
xinlabel = LABEL_RA
yinlabel = LABEL_GR
xoutlabel = LABEL_RA
youtlabel = LABEL_GR
parnames = ["radius", "pradius"]
[docs]
def morph(self, x_morph, y_morph, x_target, y_target):
"""Apply a scale factor."""
Morph.morph(self, x_morph, y_morph, x_target, y_target)
f = _spheroidalCF(x_morph, self.radius, self.pradius)
self.y_morph_out *= f
return self.xyallout
# End of class MorphSpheroid
def _sphericalCF(r, psize):
"""Spherical nanoparticle characteristic function.
From Kodama et al., Acta Cryst. A, 62, 444-453
(converted from radius to diameter).
Parameters
----------
r
Distance of interaction.
psize
The particle diameter.
"""
f = numpy.zeros_like(r)
if psize > 0:
x = r / psize
g = 1.0 - 1.5 * x + 0.5 * x * x * x
g[x > 1] = 0 # Assume zero atomic density outside particle
f += g
return f
def _spheroidalCF(r, erad, prad):
"""Spheroidal characteristic function specified using radii.
Spheroid with radii (erad, erad, prad).
Parameters
----------
prad
Polar radius.
erad
Equatorial radius.
Notes
-----
erad < prad equates to a prolate spheroid
erad > prad equates to a oblate spheroid
erad == prad is a sphere
"""
psize = 2 * erad
pelpt = prad / erad
return _spheroidalCF2(r, psize, pelpt)
def _spheroidalCF2(r, psize, axrat):
"""Spheroidal nanoparticle characteristic function.
Form factor for ellipsoid with radii (psize/2, psize/2, axrat*psize/2)
r -- distance of interaction
psize -- The equatorial diameter
axrat -- The ratio of axis lengths
From Lei et al., Phys. Rev. B, 80, 024118 (2009)
"""
pelpt = axrat
if psize <= 0 or pelpt <= 0:
return numpy.zeros_like(r)
# to simplify the equations
v = pelpt
d = psize
d2 = d * d
v2 = v * v
if v == 1: # Sphere
return _sphericalCF(r, psize)
rx = r
if v < 1: # Prolate spheroid
r = rx[rx <= v * psize]
r2 = r * r
f1 = (
1 - 3*r/(4*d*v)*(1-r2/(4*d2)*(1+2.0/(3*v2))) - 3*r/(4*d)*(1-r2/(4*d2))*v/sqrt(1-v2)*atanh(sqrt(1-v2)) # fmt: skip # noqa: E501
)
r = rx[numpy.logical_and(rx > v * psize, rx <= psize)]
r2 = r * r
# fmt: off
f2 = (
(
3*d/(8*r)*(1+r2/(2*d2))*sqrt(1-r2/d2) - 3*r/(4*d)*(1-r2/(4*d2))*atanh(sqrt(1-r2/d2)) # noqa: E501
)
* v / sqrt(1-v2)
)
# fmt: on
r = rx[rx > psize]
f3 = numpy.zeros_like(r)
f = numpy.concatenate((f1, f2, f3))
elif v > 1: # Oblate spheroid
r = rx[rx <= psize]
r2 = r * r
f1 = (
1 - 3*r/(4*d*v)*(1-r2/(4*d2)*(1+2.0/(3*v2))) - 3*r/(4*d)*(1-r2/(4*d2))*v/sqrt(v2-1)*atan(sqrt(v2-1)) # fmt: skip # noqa: E501
)
r = rx[numpy.logical_and(rx > psize, rx <= v * psize)]
r2 = r * r
f2 = (
1 - 3*r/(4*d*v)*(1-r2/(4*d2)*(1+2.0/(3*v2))) - 3.0/8*(1+r2/(2*d2))*sqrt(1-d2/r2)*v/sqrt(v2-1) - 3*r/(4*d)*(1-r2/(4*d2))*v/sqrt(v2-1)*(atan(sqrt(v2-1))-atan(sqrt(r2/d2-1))) # fmt: skip # noqa:E501
)
r = rx[rx > v * psize]
f3 = numpy.zeros_like(r)
f = numpy.concatenate((f1, f2, f3))
return f