def material_mu(name, energy, density=None, kind='total', _larch=None):
"""
material_mu(name, energy, density=None, kind='total')
return X-ray attenuation length (in 1/cm) for a material by name or formula
arguments
---------
name: chemical formul or name of material from materials list.
energy: energy or array of energies in eV
density: material density (gr/cm^3). If None, and material is a
known material, that density will be used.
kind: 'photo' or 'total' (default) for whether to
return photo-absorption or total cross-section.
returns
-------
mu, absorption length in 1/cm
notes
-----
1. material names are not case sensitive,
chemical compounds are case sensitive.
2. mu_elam() is used for mu calculation.
example
-------
>>> print material_mu('H2O', 10000.0)
5.32986401658495
"""
_materials = get_materials(_larch)
formula = None
mater = _materials.get(name.lower(), None)
if mater is not None:
formula, density = mater
else:
for key, val in _materials.items():
if name.lower() == val[0].lower(): # match formula
formula, density = val
break
# default to using passed in name as a formula
if formula is None:
formula = name
if density is None:
raise Warning('material_mu(): must give density for unknown materials')
mass_tot, mu = 0.0, 0.0
for elem, frac in chemparse(formula).items():
mass = frac * atomic_mass(elem, _larch=_larch)
mu += mass * mu_elam(elem, energy, kind=kind, _larch=_larch)
mass_tot += mass
return density*mu/mass_tot
def material_mu(name, energy, density=None, kind='total', _larch=None):
"""
material_mu(name, energy, density=None, kind='total')
return X-ray attenuation length (in 1/cm) for a material by name or formula
arguments
---------
name: chemical formul or name of material from materials list.
energy: energy or array of energies in eV
density: material density (gr/cm^3). If None, and material is a
known material, that density will be used.
kind: 'photo' or 'total' (default) for whether to
return photo-absorption or total cross-section.
returns
-------
mu, absorption length in 1/cm
notes
-----
1. material names are not case sensitive,
chemical compounds are case sensitive.
2. mu_elam() is used for mu calculation.
example
-------
>>> print(material_mu('H2O', 10000.0))
5.32986401658495
"""
_materials = get_materials(_larch)
formula = None
mater = _materials.get(name.lower(), None)
if mater is not None:
formula, density = mater
else:
for key, val in _materials.items():
if name.lower() == val[0].lower(): # match formula
formula, density = val
break
# default to using passed in name as a formula
if formula is None:
formula = name
if density is None:
raise Warning('material_mu(): must give density for unknown materials')
mass_tot, mu = 0.0, 0.0
for elem, frac in chemparse(formula).items():
mass = frac * atomic_mass(elem, _larch=_larch)
mu += mass * mu_elam(elem, energy, kind=kind, _larch=_larch)
mass_tot += mass
return density * mu / mass_tot
def __init__(self, symbol, xray_energy=None, energy_min=1500):
self.symbol = symbol
self.xray_energy = xray_energy
self.mu = 1.0
self.edges = ['K']
self.fyields = {}
if xray_energy is not None:
self.mu = mu_elam(symbol, xray_energy, kind='photo')
self.edges = []
for ename, xedge in xray_edges(self.symbol).items():
if ename.lower() in ('k', 'l1', 'l2', 'l3', 'm5'):
edge_ev = xedge.edge
if (edge_ev < xray_energy and
edge_ev > energy_min):
self.edges.append(ename)
self.fyields[ename] = xedge.fyield
# currently, we consider only one edge per element
if 'K' in self.edges:
self.edges = ['K']
if 'L3' in self.edges:
tmp = []
for ename in self.edges:
if ename.lower().startswith('l'):
tmp.append(ename)
self.edges = tmp
# apply CK corrections to fluorescent yields
if 'L3' in self.edges:
ck13 = ck_probability(symbol, 'L1', 'L3')
ck12 = ck_probability(symbol, 'L1', 'L2')
ck23 = ck_probability(symbol, 'L2', 'L3')
fy3 = self.fyields['L3']
fy2 = self.fyields.get('L2', 0)
fy1 = self.fyields.get('L1', 0)
if 'L2' in self.edges:
fy3 = fy3 + fy2*ck23
fy2 = fy2 * (1 - ck23)
if 'L1' in self.edges:
fy3 = fy3 + fy1 * (ck13 + ck12*ck23)
fy2 = fy2 + fy1 * ck12
fy1 = fy1 * (1 - ck12 - ck13)
self.fyields['L1'] = fy1
self.fyields['L2'] = fy2
self.fyields['L3'] = fy3
# look up xray lines
self.lines = {}
for ename in self.edges:
self.lines.update(xray_lines(symbol, ename))
def material_mu_components(name,
energy,
density=None,
kind='total',
_larch=None):
"""material_mu_components: absorption coefficient (in 1/cm) for a compound
arguments
---------
name: material name or compound formula
energy: energy or array of energies at which to calculate mu
density: compound density in gr/cm^3
kind: cross-section to use ('total', 'photo') for mu_elam())
returns
-------
dictionary of data for constructing mu per element,
with elements 'mass' (total mass), 'density', and
'elements' (list of atomic symbols for elements in material).
For each element, there will be an item (atomic symbol as key)
with tuple of (stoichiometric fraction, atomic mass, mu)
larch> material_mu_components('quartz', 10000)
{'Si': (1, 28.0855, 33.879432430185062), 'elements': ['Si', 'O'],
'mass': 60.0843, 'O': (2.0, 15.9994, 5.9528248152970837), 'density': 2.65}
"""
_materials = get_materials(_larch)
mater = _materials.get(name.lower(), None)
if mater is None:
formula = name
if density is None:
raise Warning(
'material_mu(): must give density for unknown materials')
else:
formula, density = mater
out = {'mass': 0.0, 'density': density, 'elements': []}
for atom, frac in chemparse(formula).items():
mass = atomic_mass(atom, _larch=_larch)
mu = mu_elam(atom, energy, kind=kind, _larch=_larch)
out['mass'] += frac * mass
out[atom] = (frac, mass, mu)
out['elements'].append(atom)
return out
def material_mu_components(name, energy, density=None, kind='total',
_larch=None):
"""material_mu_components: absorption coefficient (in 1/cm) for a compound
arguments
---------
name: material name or compound formula
energy: energy or array of energies at which to calculate mu
density: compound density in gr/cm^3
kind: cross-section to use ('total', 'photo') for mu_elam())
returns
-------
dictionary of data for constructing mu per element,
with elements 'mass' (total mass), 'density', and
'elements' (list of atomic symbols for elements in material).
For each element, there will be an item (atomic symbol as key)
with tuple of (stoichiometric fraction, atomic mass, mu)
larch> material_mu_components('quartz', 10000)
{'Si': (1, 28.0855, 33.879432430185062), 'elements': ['Si', 'O'],
'mass': 60.0843, 'O': (2.0, 15.9994, 5.9528248152970837), 'density': 2.65}
"""
_materials = get_materials(_larch)
mater = _materials.get(name.lower(), None)
if mater is None:
formula = name
if density is None:
raise Warning('material_mu(): must give density for unknown materials')
else:
formula, density = mater
out = {'mass': 0.0, 'density': density, 'elements':[]}
for atom, frac in chemparse(formula).items():
mass = atomic_mass(atom, _larch=_larch)
mu = mu_elam(atom, energy, kind=kind, _larch=_larch)
out['mass'] += frac*mass
out[atom] = (frac, mass, mu)
out['elements'].append(atom)
return out
def concentration_resid(pars,
lineData=None,
mca=None,
phiPrime=np.pi / 2.,
phiDblPrime=np.pi / 2.,
xray_energy=30000.,
larch=None):
cscPhiPrime = 1. / np.sin(phiPrime)
cscPhiDblPrime = 1. / np.sin(phiDblPrime)
energy = mca.get_energy() * 1000.
dE = energy[1] - energy[0]
probeSpectrum = np.zeros(len(energy))
ind = index_of(energy, xray_energy)
probeSpectrum[ind] = 1.0
C = np.array([pars[elem + '_con'].value for elem in lineData], ndmin=2).T
Cal = np.array([pars[elem + '_cal'].value for elem in lineData])
Intensity = np.array([lineData[elem][2] for elem in lineData])
mu = np.zeros((len(lineData) + 1, len(energy)))
for i, elem_i in enumerate(lineData):
mu[i, :] = mu_elam(elem_i, energy, kind='total', _larch=larch)
mu[-1, :] += C[i, 0] * mu[i, :]
beta = np.zeros((len(lineData), len(lineData), len(energy)))
delta = np.zeros((len(lineData), len(lineData), len(energy)))
for i, elem_i in enumerate(lineData):
line_en_i = lineData[elem_i][1]
edge_i = lineData[elem_i][0][len(elem_i)].title()
edge_en_i, _, r_i = xray_edge(elem_i, edge_i, _larch=larch)
for j, elem_j in enumerate(lineData):
line_en_j = lineData[elem_j][1]
edge_j = lineData[elem_j][0][len(elem_j)].title()
line_j = lineData[elem_j][0][len(elem_j):].title()
edge_en_j, _, r_j = xray_edge(elem_j, edge_j, _larch=larch)
yield_j, _, prob_j = fluo_yield(elem_j,
edge_j,
line_j,
np.max(energy),
_larch=larch)
k_j = prob_j * yield_j * (r_j - 1.) / r_j
mu_s_prime = mu[-1, :] * cscPhiPrime
mu_s_line_en_j = np.interp(line_en_j, energy, mu[-1, :])
mu_s_dblPrime_line_en_i = np.interp(line_en_i, energy,
mu[-1, :]) * cscPhiDblPrime
P_ij = np.log(1. + mu_s_prime / mu_s_line_en_j) / mu_s_prime + \
np.log(1. + mu_s_dblPrime_line_en_i / mu_s_line_en_j) / mu_s_dblPrime_line_en_i
beta[i,j,:] = mu[j,:] * cscPhiPrime + \
np.interp(line_en_i, energy, mu[j,:]) * cscPhiDblPrime
beta[i,j,:] /= mu[i,:] * cscPhiPrime + \
np.interp(line_en_i, energy, mu[i,:]) * cscPhiDblPrime
beta[i, j, :] -= 1.
delta[i, j, :] = np.where(energy >= edge_en_j, 0.5, 0.0)
if line_en_j <= edge_en_i: delta[i, j, :] *= 0.
delta[i, j, :] *= k_j
delta[i, j, :] *= mu[j, :] * cscPhiPrime
delta[i, j, :] *= np.interp(line_en_j, energy, mu[i, :])
delta[i,j,:] /= (mu[-1,:] * cscPhiPrime) + \
(np.interp(line_en_i, energy, mu[-1,:]) * cscPhiDblPrime)
delta[i, j, :] *= P_ij
W = np.zeros((1, len(lineData), len(energy)))
for i, elem in enumerate(lineData):
line_en_i = lineData[elem_i][1]
mu_i_star = mu[i,:] * cscPhiPrime +\
np.interp(line_en_i, energy, mu[i,:]) * cscPhiDblPrime
W[0, i, :] = mu[i, :] * probeSpectrum * dE
W[0, i, :] /= mu_i_star * (1 + np.sum(C * beta[i, :, :], axis=0))
alpha = np.sum(W * beta, axis=2) / np.sum(W, axis=2)
epsilon = np.sum(W * delta, axis=2) / np.sum(W, axis=2)
num = 1 + np.sum(C.T * epsilon, axis=1)
den = 1 + np.sum(C.T * alpha, axis=1)
C = np.reshape(C, (len(C)))
print(pars['cu_con'].value, pars['zn_con'].value, pars['mn_con'].value)
return Intensity - Cal * C * num / den
