def f2(element, energy):
"""
The imaginery part of anomalous X-ray scattering factor for
selected input energy (or energies) in eV.
using xraylib backend
Parameters:
element : Name, Symbol or Atomic Number (Z) as input
energy : energy in keV - scalar, list, tuple or numpy array
Returns:
f2 : float or numpy array - same size as input energy
imaginery part of anomalous X-ray scattering factor at input
energy or energies
"""
z = elementDB[element]["Z"]
if isinstance(energy, (list, tuple, np.ndarray)):
f2 = np.zeroslike(energy)
for i,enrg in enumerate(energy):
f2[i] = xraylib.Fii(z,enrg)
else:
f2 = xraylib.Fii(z,enrg)
return f2
def Fii(ID,E=None):
if E==None:
E=pypsepics.get("SIOC:SYS0:ML00:AO627")/1000
E=eV(E)/1000
z=elementZ[ID]
f=xraylib.Fii(z,E)
return f
def reflectivity(descriptor,energy,theta,density=None,rough=0.0):
if isinstance(descriptor,str):
Z = xraylib.SymbolToAtomicNumber(descriptor)
symbol = descriptor
else:
Z = descriptor
symbol = xraylib.AtomicNumberToSymbol(descriptor)
if density == None:
density = xraylib.ElementDensity(Z)
atwt = xraylib.AtomicWeight(Z)
avogadro = codata.Avogadro
toangstroms = codata.h * codata.c / codata.e * 1e10
re = codata.e**2 / codata.m_e / codata.c**2 / (4*numpy.pi*codata.epsilon_0) * 1e2 # in cm
molecules_per_cc = density * avogadro / atwt
wavelength = toangstroms / energy * 1e-8 # in cm
k = molecules_per_cc * re * wavelength * wavelength / 2.0 / numpy.pi
f1 = numpy.zeros_like(energy)
f2 = numpy.zeros_like(energy)
for i,ienergy in enumerate(energy):
f1[i] = Z + xraylib.Fi(Z,1e-3*ienergy)
f2[i] = - xraylib.Fii(Z,1e-3*ienergy)
alpha = 2.0 * k * f1
gamma = 2.0 * k * f2
rs,rp,runp = interface_reflectivity(alpha,gamma,theta)
if rough != 0:
rough *= 1e-8 # to cm
debyewaller = numpy.exp( -( 4.0 * numpy.pi * numpy.sin(theta) * rough / wavelength)**2)
else:
debyewaller = 1.0
return rs*debyewaller,rp*debyewaller,runp*debyewaller
def new_bragg(cls,
DESCRIPTOR="Graphite",
H_MILLER_INDEX=0,
K_MILLER_INDEX=0,
L_MILLER_INDEX=2,
TEMPERATURE_FACTOR=1.0,
E_MIN=5000.0,
E_MAX=15000.0,
E_STEP=100.0,
SHADOW_FILE="bragg.dat"):
"""
SHADOW preprocessor for crystals - python+xraylib version
-"""
# retrieve physical constants needed
codata = scipy.constants.codata.physical_constants
codata_e2_mc2, tmp1, tmp2 = codata["classical electron radius"]
# or, hard-code them
# In [179]: print("codata_e2_mc2 = %20.11e \n" % codata_e2_mc2 )
# codata_e2_mc2 = 2.81794032500e-15
fileout = SHADOW_FILE
descriptor = DESCRIPTOR
hh = int(H_MILLER_INDEX)
kk = int(K_MILLER_INDEX)
ll = int(L_MILLER_INDEX)
temper = float(TEMPERATURE_FACTOR)
emin = float(E_MIN)
emax = float(E_MAX)
estep = float(E_STEP)
#
# end input section, start calculations
#
f = open(fileout, 'wt')
cryst = xraylib.Crystal_GetCrystal(descriptor)
volume = cryst['volume']
#test crystal data - not needed
itest = 1
if itest:
if (cryst == None):
sys.exit(1)
print(" Unit cell dimensions are %f %f %f" %
(cryst['a'], cryst['b'], cryst['c']))
print(" Unit cell angles are %f %f %f" %
(cryst['alpha'], cryst['beta'], cryst['gamma']))
print(" Unit cell volume is %f A^3" % volume)
print(" Atoms at:")
print(" Z fraction X Y Z")
for i in range(cryst['n_atom']):
atom = cryst['atom'][i]
print(" %3i %f %f %f %f" %
(atom['Zatom'], atom['fraction'], atom['x'], atom['y'],
atom['z']))
print(" ")
volume = volume * 1e-8 * 1e-8 * 1e-8 # in cm^3
#flag ZincBlende
f.write("%i " % 0)
#1/V*electronRadius
f.write("%e " % ((1e0 / volume) * (codata_e2_mc2 * 1e2)))
#dspacing
dspacing = xraylib.Crystal_dSpacing(cryst, hh, kk, ll)
f.write("%e " % (dspacing * 1e-8))
f.write("\n")
#Z's
atom = cryst['atom']
f.write("%i " % atom[0]["Zatom"])
f.write("%i " % atom[-1]["Zatom"])
f.write("%e " % temper) # temperature parameter
f.write("\n")
ga = (1e0+0j) + cmath.exp(1j*cmath.pi*(hh+kk)) \
+ cmath.exp(1j*cmath.pi*(hh+ll)) \
+ cmath.exp(1j*cmath.pi*(kk+ll))
gb = ga * cmath.exp(1j * cmath.pi * 0.5 * (hh + kk + ll))
ga_bar = ga.conjugate()
gb_bar = gb.conjugate()
f.write("(%20.11e,%20.11e ) \n" % (ga.real, ga.imag))
f.write("(%20.11e,%20.11e ) \n" % (ga_bar.real, ga_bar.imag))
f.write("(%20.11e,%20.11e ) \n" % (gb.real, gb.imag))
f.write("(%20.11e,%20.11e ) \n" % (gb_bar.real, gb_bar.imag))
zetas = numpy.array([atom[0]["Zatom"], atom[-1]["Zatom"]])
for zeta in zetas:
xx01 = 1e0 / 2e0 / dspacing
xx00 = xx01 - 0.1
xx02 = xx01 + 0.1
yy00 = xraylib.FF_Rayl(int(zeta), xx00)
yy01 = xraylib.FF_Rayl(int(zeta), xx01)
yy02 = xraylib.FF_Rayl(int(zeta), xx02)
xx = numpy.array([xx00, xx01, xx02])
yy = numpy.array([yy00, yy01, yy02])
fit = numpy.polyfit(xx, yy, 2)
#print "zeta: ",zeta
#print "z,xx,YY: ",zeta,xx,yy
#print "fit: ",fit[::-1] # reversed coeffs
#print "fit-tuple: ",(tuple(fit[::-1].tolist())) # reversed coeffs
#print("fit-tuple: %e %e %e \n" % (tuple(fit[::-1].tolist())) ) # reversed coeffs
f.write("%e %e %e \n" %
(tuple(fit[::-1].tolist()))) # reversed coeffs
npoint = int((emax - emin) / estep + 1)
f.write(("%i \n") % npoint)
for i in range(npoint):
energy = (emin + estep * i)
f1a = xraylib.Fi(int(zetas[0]), energy * 1e-3)
f2a = xraylib.Fii(int(zetas[0]), energy * 1e-3)
f1b = xraylib.Fi(int(zetas[1]), energy * 1e-3)
f2b = xraylib.Fii(int(zetas[1]), energy * 1e-3)
out = numpy.array([energy, f1a, abs(f2a), f1b, abs(f2b)])
f.write(("%20.11e %20.11e %20.11e \n %20.11e %20.11e \n") %
(tuple(out.tolist())))
f.close()
print("File written to disk: %s" % fileout)
def bragg():
"""
SHADOW preprocessor for crystals - python+xraylib version
-"""
# retrieve physical constants needed
codata = scipy.constants.codata.physical_constants
codata_e2_mc2, tmp1, tmp2 = codata["classical electron radius"]
# or, hard-code them
# In [179]: print("codata_e2_mc2 = %20.11e \n" % codata_e2_mc2 )
# codata_e2_mc2 = 2.81794032500e-15
print("bragg: SHADOW preprocessor for crystals - python+xraylib version")
fileout = raw_input("Name of output file : ")
f = open(fileout, 'wb')
print(" bragg (python) only works now for ZincBlende Cubic structures. ")
print(" Valid descriptor are: ")
print(" Si (alternatiovely Si_NIST, Si2) ")
print(" Ge")
print(" Diamond")
print(" GaAs, GaSb, GaP")
print(" InAs, InP, InSb")
print(" SiC")
descriptor = raw_input("Name of crystal descriptor : ")
cryst = xraylib.Crystal_GetCrystal(descriptor)
#test crystal data - not needed
itest = 1
if itest:
if (cryst == None):
sys.exit(1)
print " Unit cell dimensions are %f %f %f" % (cryst['a'],cryst['b'],cryst['c'])
print " Unit cell angles are %f %f %f" % (cryst['alpha'],cryst['beta'],cryst['gamma'])
volume = cryst['volume']
print " Unit cell volume is %f" % volume
volume = volume*1e-8*1e-8*1e-8 # in cm^3
print " Atoms at:"
print " Z fraction X Y Z"
for i in range(cryst['n_atom']):
atom = cryst['atom'][i]
print " %3i %f %f %f %f" % (atom['Zatom'], atom['fraction'], atom['x'], atom['y'], atom['z'])
print " "
print("Miller indices of crystal plane of reflection.")
miller = raw_input("H K L: ")
miller = miller.split()
hh = int(miller[0])
kk = int(miller[1])
ll = int(miller[2])
#flag ZincBlende
f.write( "%i " % 0)
#1/V*electronRadius
f.write( "%e " % ((1e0/volume)*(codata_e2_mc2*1e2)) )
#dspacing
dspacing = xraylib.Crystal_dSpacing(cryst, hh, kk, ll)
f.write( "%e " % (dspacing*1e-8) )
f.write( "\n")
#Z's
atom = cryst['atom']
f.write( "%i " % atom[0]["Zatom"] )
f.write( "%i " % atom[7]["Zatom"] )
temper = raw_input("Temperature (Debye-Waller) factor (set 1 for default): ")
temper = float(temper)
f.write( "%e " % temper ) # temperature parameter
f.write( "\n")
ga = (1e0+0j) + cmath.exp(1j*cmath.pi*(hh+kk)) \
+ cmath.exp(1j*cmath.pi*(hh+ll)) \
+ cmath.exp(1j*cmath.pi*(kk+ll))
gb = ga * cmath.exp(1j*cmath.pi*0.5*(hh+kk+ll))
ga_bar = ga.conjugate()
gb_bar = gb.conjugate()
f.write( "(%20.11e,%20.11e ) \n" % (ga.real, ga.imag) )
f.write( "(%20.11e,%20.11e ) \n" % (ga_bar.real, ga_bar.imag) )
f.write( "(%20.11e,%20.11e ) \n" % (gb.real, gb.imag) )
f.write( "(%20.11e,%20.11e ) \n" % (gb_bar.real, gb_bar.imag) )
zetas = numpy.array([atom[0]["Zatom"],atom[7]["Zatom"]])
for zeta in zetas:
xx01 = 1e0/2e0/dspacing
xx00 = xx01-0.1
xx02 = xx01+0.1
yy00= xraylib.FF_Rayl(int(zeta),xx00)
yy01= xraylib.FF_Rayl(int(zeta),xx01)
yy02= xraylib.FF_Rayl(int(zeta),xx02)
xx = numpy.array([xx00,xx01,xx02])
yy = numpy.array([yy00,yy01,yy02])
fit = numpy.polyfit(xx,yy,2)
#print "zeta: ",zeta
#print "z,xx,YY: ",zeta,xx,yy
#print "fit: ",fit[::-1] # reversed coeffs
#print "fit-tuple: ",(tuple(fit[::-1].tolist())) # reversed coeffs
#print("fit-tuple: %e %e %e \n" % (tuple(fit[::-1].tolist())) ) # reversed coeffs
f.write("%e %e %e \n" % (tuple(fit[::-1].tolist())) ) # reversed coeffs
emin = raw_input("minimum photon energy (eV): ")
emin = float(emin)
emax = raw_input("maximum photon energy (eV): ")
emax = float(emax)
estep = raw_input("energy step (eV): ")
estep = float(estep)
npoint = int( (emax - emin)/estep + 1 )
f.write( ("%i \n") % npoint)
for i in range(npoint):
energy = (emin+estep*i)
f1a = xraylib.Fi(int(zetas[0]),energy*1e-3)
f2a = xraylib.Fii(int(zetas[0]),energy*1e-3)
f1b = xraylib.Fi(int(zetas[1]),energy*1e-3)
f2b = xraylib.Fii(int(zetas[1]),energy*1e-3)
out = numpy.array([energy,f1a,abs(f2a),f1b,abs(f2b)])
f.write( ("%20.11e %20.11e %20.11e \n %20.11e %20.11e \n") % ( tuple(out.tolist()) ) )
f.close()
print("File written to disk: %s" % fileout)
return None
print("CS2 Refractive Index at 10.0 keV : {} - {} i".format(xraylib.Refractive_Index_Re("CS2",10.0,1.261), xraylib.Refractive_Index_Im("CS2",10.0,1.261)))
print("C16H14O3 Refractive Index at 1 keV : {} - {} i".format(xraylib.Refractive_Index_Re("C16H14O3",1.0,1.2), xraylib.Refractive_Index_Im("C16H14O3",1.0,1.2)))
print("SiO2 Refractive Index at 5 keV : {} - {} i".format(xraylib.Refractive_Index_Re("SiO2",5.0,2.65), xraylib.Refractive_Index_Im("SiO2",5.0,2.65)))
print("Compton profile for Fe at pz = 1.1 : {}".format(xraylib.ComptonProfile(26,1.1)))
print("M5 Compton profile for Fe at pz = 1.1 : {}".format(xraylib.ComptonProfile_Partial(26, xraylib.M5_SHELL,1.1)))
print("M1->M5 Coster-Kronig transition probability for Au : {}".format(xraylib.CosKronTransProb(79, xraylib.FM15_TRANS)))
print("L1->L3 Coster-Kronig transition probability for Fe : {}".format(xraylib.CosKronTransProb(26, xraylib.FL13_TRANS)))
print("Au Ma1 XRF production cs at 10.0 keV (Kissel): {}".format(xraylib.CS_FluorLine_Kissel(79, xraylib.MA1_LINE,10.0)))
print("Au Mb XRF production cs at 10.0 keV (Kissel): {}".format(xraylib.CS_FluorLine_Kissel(79, xraylib.MB_LINE,10.0)))
print("Au Mg XRF production cs at 10.0 keV (Kissel): {}".format(xraylib.CS_FluorLine_Kissel(79, xraylib.MG_LINE,10.0)))
print("K atomic level width for Fe: {}".format(xraylib.AtomicLevelWidth(26, xraylib.K_SHELL)))
print("Bi L2-M5M5 Auger non-radiative rate: {}".format(xraylib.AugerRate(86, xraylib.L2_M5M5_AUGER)))
print("Bi L3 Auger yield: {}".format(xraylib.AugerYield(86, xraylib.L3_SHELL)))
print("Sr anomalous scattering factor Fi at 10.0 keV: {}".format(xraylib.Fi(38, 10.0)))
print("Sr anomalous scattering factor Fii at 10.0 keV: {}".format(xraylib.Fii(38, 10.0)))
symbol = xraylib.AtomicNumberToSymbol(26)
print("Symbol of element 26 is: {}".format(symbol))
print("Number of element Fe is: {}".format(xraylib.SymbolToAtomicNumber("Fe")))
Z = np.array([26])
symbol = xraylib.AtomicNumberToSymbol(Z[0])
print("Symbol of element 26 is: {}".format(symbol))
print("Pb Malpha XRF production cs at 20.0 keV with cascade effect: {}".format(xraylib.CS_FluorLine_Kissel(82, xraylib.MA1_LINE,20.0)))
print("Pb Malpha XRF production cs at 20.0 keV with radiative cascade effect: {}".format(xraylib.CS_FluorLine_Kissel_Radiative_Cascade(82, xraylib.MA1_LINE,20.0)))
print("Pb Malpha XRF production cs at 20.0 keV with non-radiative cascade effect: {}".format(xraylib.CS_FluorLine_Kissel_Nonradiative_Cascade(82, xraylib.MA1_LINE,20.0)))
print("Pb Malpha XRF production cs at 20.0 keV without cascade effect: {}".format(xraylib.CS_FluorLine_Kissel_no_Cascade(82, xraylib.MA1_LINE,20.0)))
print("Al mass energy-absorption cs at 20.0 keV: {}".format(xraylib.CS_Energy(13, 20.0)))
print("Pb mass energy-absorption cs at 40.0 keV: {}".format(xraylib.CS_Energy(82, 40.0)))
print("CdTe mass energy-absorption cs at 40.0 keV: {}".format(xraylib.CS_Energy_CP("CdTe", 40.0)))
print("Au Ma1 XRF production cs at 10.0 keV (Kissel): {}".format(
xraylib.CS_FluorLine_Kissel(79, xraylib.MA1_LINE, 10.0)))
print("Au Mb XRF production cs at 10.0 keV (Kissel): {}".format(
xraylib.CS_FluorLine_Kissel(79, xraylib.MB_LINE, 10.0)))
print("Au Mg XRF production cs at 10.0 keV (Kissel): {}".format(
xraylib.CS_FluorLine_Kissel(79, xraylib.MG_LINE, 10.0)))
print("K atomic level width for Fe: {}".format(
xraylib.AtomicLevelWidth(26, xraylib.K_SHELL)))
print("Bi L2-M5M5 Auger non-radiative rate: {}".format(
xraylib.AugerRate(86, xraylib.L2_M5M5_AUGER)))
print("Bi L3 Auger yield: {}".format(xraylib.AugerYield(86, xraylib.L3_SHELL)))
print("Sr anomalous scattering factor Fi at 10.0 keV: {}".format(
xraylib.Fi(38, 10.0)))
print("Sr anomalous scattering factor Fii at 10.0 keV: {}".format(
xraylib.Fii(38, 10.0)))
symbol = xraylib.AtomicNumberToSymbol(26)
print("Symbol of element 26 is: {}".format(symbol))
print("Number of element Fe is: {}".format(xraylib.SymbolToAtomicNumber("Fe")))
Z = np.array([26])
symbol = xraylib.AtomicNumberToSymbol(Z[0])
print("Symbol of element 26 is: {}".format(symbol))
print("Pb Malpha XRF production cs at 20.0 keV with cascade effect: {}".format(
xraylib.CS_FluorLine_Kissel(82, xraylib.MA1_LINE, 20.0)))
print(
"Pb Malpha XRF production cs at 20.0 keV with radiative cascade effect: {}"
.format(
xraylib.CS_FluorLine_Kissel_Radiative_Cascade(82, xraylib.MA1_LINE,
20.0)))
print(
def test_refractiveindex(self):
density = float(2.328)
c = compoundfromformula.CompoundFromFormula("Si", density, name="silicon")
energy = np.asarray([5, 10], dtype=float)
Z = 14
# Xraylib (TODO: n_im sign is wrong!)
n_re0 = np.asarray(
[xraylib.Refractive_Index_Re("Si", e, density) for e in energy]
)
n_im0 = -np.asarray(
[xraylib.Refractive_Index_Im("Si", e, density) for e in energy]
)
# Exactly like Xraylib (TODO: CS_Total -> CS_Photo_Total)
delta = (
density
* 4.15179082788e-4
* (Z + np.asarray([xraylib.Fi(Z, e) for e in energy]))
/ xraylib.AtomicWeight(Z)
/ energy ** 2
)
beta = (
np.asarray([xraylib.CS_Total(Z, e) for e in energy])
* density
* 9.8663479e-9
/ energy
)
n_re1 = 1 - delta
n_im1 = -beta
np.testing.assert_allclose(n_re0, n_re1)
np.testing.assert_allclose(n_im0, n_im1)
# Im: Kissel
n_im1b = (
-np.asarray([xraylib.CS_Total_Kissel(Z, e) for e in energy])
* density
* 9.8663479e-9
/ energy
)
# Im: Kissel with pint
n_im1d = (
ureg.Quantity(c.mass_att_coeff(energy), "cm^2/g")
* ureg.Quantity(c.density, "g/cm^3")
* ureg.Quantity(energy, "keV").to("cm", "spectroscopy")
/ (4 * np.pi)
)
n_im1d = -n_im1d.to("dimensionless").magnitude
r = n_im1b / n_im1d
np.testing.assert_allclose(r, r[0])
# Im: other formula
n_im1c = (
density
* 4.15179082788e-4
* (np.asarray([xraylib.Fii(Z, e) for e in energy]))
/ xraylib.AtomicWeight(Z)
/ energy ** 2
)
# Spectrocrunch
n_re2 = c.refractive_index_real(energy)
n_im2 = c.refractive_index_imag(energy)
np.testing.assert_allclose(n_re2, n_re0)
np.testing.assert_allclose(n_im2, n_im1c, rtol=1e-6)