def profile(self, extra=False):
"""
Calculates the volume fraction profile
Returns
-------
z, vfp : np.ndarray
Distance from the interface, volume fraction profile
"""
s = Structure()
s |= SLD(0)
m = SLD(1.)
for i, slab in enumerate(self.left_slabs):
layer = m(slab.thick.value, slab.rough.value)
if not i:
layer.rough.value = 0
layer.vfsolv.value = slab.vfsolv.value
s |= layer
polymer_slabs = self.slabs()
offset = np.sum(s.slabs()[:, 0])
if polymer_slabs is not None:
for i in range(np.size(polymer_slabs, 0)):
layer = m(polymer_slabs[i, 0], polymer_slabs[i, 3])
layer.vfsolv.value = polymer_slabs[i, -1]
s |= layer
for i, slab in enumerate(self.right_slabs):
layer = m(slab.thick.value, slab.rough.value)
layer.vfsolv.value = 1 - slab.vfsolv.value
s |= layer
s |= SLD(0, 0)
# now calculate the VFP.
total_thickness = np.sum(s.slabs()[:, 0])
zed = np.linspace(0, total_thickness, total_thickness + 1)
# SLD profile puts a very small roughness on the interfaces with zero
# roughness.
zed[0] = 0.01
z, s = s.sld_profile(z=zed)
s[0] = s[1]
# perhaps you'd like to plot the knot locations
zeds = np.cumsum(self.dz)
if np.sum(self.dz) > 1:
zeds /= np.sum(self.dz)
zeds = np.clip(zeds, 0, 1)
zed_knots = zeds * float(self.extent) + offset
if extra:
return z, s, zed_knots, np.array(self.vf)
else:
return z, s
def phase_problem_plot(flag):
if flag != "SLD" and flag != "ACF":
raise Exception("Invalid flag to plot")
qvals = np.linspace(0,0.2,1025)[1:]
sld1 = SLD(0, 0)
sld3 = SLD(2.074, 0)
layer1 = sld1(0, 0)
layer3 = sld3(0, 0)
fig = plt.figure(figsize=(15, 10))
gs = gridspec.GridSpec(2, 2)
ax1 = plt.subplot(gs[0,0])
ax2 = plt.subplot(gs[1,0])
for i, style in zip([0,1.0], ['k-', 'r:']):
sld20 = SLD(6.335 - i, 0)
sld21 = SLD(6.335 + i, 0)
layer20 = sld20(100, 0)
layer21 = sld21(100, 0)
structure = Structure(layer1 | layer20 | layer21 | layer3)
z, rho = structure.sld_profile()
drho = (rho[1:] - rho[:-1]) / (z[1:] - z[:-1])
z_ = 0.5 * (z[:-1] + z[1:])
acf = autocorr(drho)
z_acf = z_ - z_.min()
z_acf = np.hstack((-np.flip(z_acf)[:-1], z_acf))
if flag == 'SLD':
ax1.plot(z, rho, style)
ax2.semilogy(qvals, ReflectModel(structure, dq=0.0).model(qvals), style)
else:
ax1.stem(z_, drho, style, markerfmt=' ', basefmt=style, use_line_collection=True)
ax2.stem(z_acf, acf, style, markerfmt=' ', basefmt=style, use_line_collection=True)
if flag == 'SLD':
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
ax2.set_xlabel(r'$q$/Å')
ax2.set_ylabel(r'$R(q)$')
else:
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho\'(z)$/Å$^{-3}$')
ax2.set_xlabel(r'$z$/Å')
ax2.set_ylabel("$ \\rm{ACF}_{\\rho'}(z)/ \\AA^{-5}$")
plt.tight_layout()
figfilename = f"phase_problem_{flag}.pdf"
plt.savefig(figfilename)
print(f"Figure saved as {figfilename}")
plt.close()
def roughness():
sld1 = SLD(0, 0)
sld2 = SLD(6.335, 0)
sld3 = SLD(2.074, 0)
layer1 = sld1(0, 0)
layer3 = sld3(10, 0)
fig = plt.figure(figsize=(10, 7.5 / 2))
gs = gridspec.GridSpec(1, 3)
ax1 = plt.subplot(gs[0:2])
ax2 = plt.subplot(gs[2])
for i in range(3, 9, 2):
layer2 = sld2(10, i)
structure = Structure(layer1 | layer2 | layer3)
ax1.plot(*structure.sld_profile())
ax2.plot(*structure.sld_profile())
ax2.set_ylim(1.6, 2.6)
ax2.set_xlim(5, 15)
ax1.axhline(sld3.real, color='k', alpha=0.3)
ax2.axhline(sld3.real, color='k', alpha=0.3)
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
ax1.text(0.025,
0.95,
'(a)',
horizontalalignment='left',
verticalalignment='top',
transform=ax1.transAxes)
ax2.set_xlabel(r'$z$/Å')
ax2.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
ax2.text(0.025,
0.95,
'(b)',
horizontalalignment='left',
verticalalignment='top',
transform=ax2.transAxes)
plt.tight_layout()
plt.savefig("roughness.pdf")
plt.close()
sld1 = SLD(0, 0)
sld2 = SLD(6.335, 0)
sld3 = SLD(2.074, 0)
layer1 = sld1(0, 0)
layer3 = sld3(10, 0)
fig = plt.figure(figsize=(10, 7.5 / 2))
gs = gridspec.GridSpec(1, 3)
ax1 = plt.subplot(gs[0:2])
ax2 = plt.subplot(gs[2])
for i in range(3, 9, 2):
layer2 = sld2(10, i)
structure = Structure(layer1 | layer2 | layer3)
ax1.plot(*structure.sld_profile())
ax2.plot(*structure.sld_profile())
ax2.set_ylim(1.6, 2.6)
ax2.set_xlim(5, 15)
ax1.axhline(sld3.real, color='k', alpha=0.3)
ax2.axhline(sld3.real, color='k', alpha=0.3)
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
ax1.text(0.025,
0.95,
'(a)',
horizontalalignment='left',
verticalalignment='top',
transform=ax1.transAxes)
ax2.set_xlabel(r'$z$/Å')
ax2.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
def phase_problem_plot(flag):
if flag != "SLD" and flag != "ACF":
raise Exception("Invalid flag to plot")
qvals = np.linspace(0, 0.2, 1025)[1:]
sld1 = SLD(0, 0)
sld3 = SLD(2.074, 0)
layer1 = sld1(0, 0)
layer3 = sld3(0, 0)
fig = plt.figure(figsize=(10, 7.5))
gs = gridspec.GridSpec(2, 1)
ax1 = plt.subplot(gs[0, 0])
ax2 = plt.subplot(gs[1, 0])
colors = [_fig_params.colors[0], _fig_params.colors[1]]
ls = ['-', ':']
for i in [0, 1]:
sld20 = SLD(6.335 - i, 0)
sld21 = SLD(6.335 + i, 0)
layer20 = sld20(100, 0)
layer21 = sld21(100, 0)
structure = Structure(layer1 | layer20 | layer21 | layer3)
z, rho = structure.sld_profile()
drho = (rho[1:] - rho[:-1]) / (z[1:] - z[:-1])
z_ = 0.5 * (z[:-1] + z[1:])
acf = autocorr(drho)
z_acf = z_ - z_.min()
z_acf = np.hstack((-np.flip(z_acf)[:-1], z_acf))
if flag == 'SLD':
ax1.plot(z, rho, color=colors[i], ls=ls[i])
ax2.semilogy(qvals,
ReflectModel(structure, dq=0.0).model(qvals),
color=colors[i],
ls=ls[i])
else:
ax1.stem(z_,
drho,
linefmt='C{}'.format(i) + ls[i],
basefmt='C{}'.format(i) + ls[i],
markerfmt=' ',
use_line_collection=True)
ax2.stem(z_acf,
acf,
linefmt='C{}'.format(i) + ls[i],
basefmt='C{}'.format(i) + ls[i],
markerfmt=' ',
use_line_collection=True)
if flag == 'SLD':
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho(z)$/Å$^{-2}$')
ax2.set_xlabel(r'$q$/Å')
ax2.set_ylabel(r'$R(q)$')
ax1.text(0.025,
0.95,
'(a)',
horizontalalignment='left',
verticalalignment='top',
transform=ax1.transAxes)
else:
ax1.set_xlabel(r'$z$/Å')
ax1.set_ylabel(r'$\rho\'(z)$/Å$^{-3}$')
ax2.set_xlabel(r'$z$/Å')
ax2.set_ylabel("$ \\rm{ACF}_{\\rho'}(z)/ \\AA^{-5}$")
ax1.text(0.975,
0.95,
'(a)',
horizontalalignment='right',
verticalalignment='top',
transform=ax1.transAxes)
ax2.text(0.975,
0.95,
'(b)',
horizontalalignment='right',
verticalalignment='top',
transform=ax2.transAxes)
plt.tight_layout()
figfilename = f"phase_problem_{flag}.pdf"
plt.savefig(figfilename)
print(f"Figure saved as {figfilename}")
plt.close()