1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
|
import numpy as np
from numpy import pi, isnan
from numpy.testing import assert_almost_equal
from periodictable import formula
from periodictable import Cu,Mo,Ni,Fe,Si,H,D,O
from periodictable.xsf import xray_energy, xray_sld_from_atoms, xray_sld
from periodictable.xsf import index_of_refraction, mirror_reflectivity
def test_xsf():
# Check some K_alpha and K_beta1 values
assert Cu.K_alpha == 1.5418
assert Cu.K_beta1 == 1.3922
# Check scalar scattering factor lookup
f1,f2 = Ni.xray.scattering_factors(energy=xray_energy(Cu.K_alpha))
assert_almost_equal(f1, 25.0229, 4)
assert_almost_equal(f2, 0.5249, 4)
# Check array scattering factor lookup
f1,f2 = Ni.xray.scattering_factors(wavelength=Cu.K_alpha)
m1,m2 = Ni.xray.scattering_factors(wavelength=Mo.K_alpha)
B1,B2 = Ni.xray.scattering_factors(wavelength=[Cu.K_alpha,Mo.K_alpha])
assert (B1==[f1,m1]).all() and (B2==[f2,m2]).all()
# Check that we can lookup sld by wavelength and energy
Fe_rho,Fe_mu = Fe.xray.sld(wavelength=Cu.K_alpha)
assert_almost_equal(Fe_rho, 59.45, 2)
Si_rho,Si_mu = Si.xray.sld(energy=8.050)
assert_almost_equal(Si_rho, 20.0705, 4)
assert_almost_equal(Si_mu, 0.4572, 4)
# Check that wavelength is the default
Fe_rho_default,Fe_mu_default = Fe.xray.sld(wavelength=Cu.K_alpha)
assert Fe_rho == Fe_rho_default and Fe_mu == Fe_mu_default
# Check array form of sld lookup
f1,f2 = Si.xray.sld(wavelength=Cu.K_alpha)
m1,m2 = Si.xray.sld(wavelength=Mo.K_alpha)
B1,B2 = Si.xray.sld(wavelength=[Cu.K_alpha,Mo.K_alpha])
assert (B1==[f1,m1]).all() and (B2==[f2,m2]).all()
# Check energy conversion is consistent
f1,f2 = Si.xray.sld(energy=xray_energy(Cu.K_alpha))
m1,m2 = Si.xray.sld(energy=xray_energy(Mo.K_alpha))
assert (B1==[f1,m1]).all() and (B2==[f2,m2]).all()
B1,B2 = Si.xray.sld(energy=xray_energy([Cu.K_alpha,Mo.K_alpha]))
assert (B1==[f1,m1]).all() and (B2==[f2,m2]).all()
#print Cu.xray.sftable
#plot_xsf(Cu)
#emission_table()
#sld_table(table,Cu.K_alpha)
"""
# Table of scattering length densities for various molecules
for molecule,density in [('SiO2',2.2),('B4C',2.52)]:
atoms = formula(molecule).atoms
rho,mu = xray_sld(atoms,density,wavelength=Cu.K_alpha)
print "sld for %s(%g g/cm**3) rho=%.4g mu=%.4g"\
%(molecule,density,rho,mu)
"""
# Cross check against mo
rho,mu = xray_sld({Si:1},density=Si.density,wavelength=1.54)
rhoSi,muSi = Si.xray.sld(wavelength=1.54)
assert_almost_equal(rho, rhoSi, 14)
assert_almost_equal(mu, muSi, 14)
# Check that xray_sld works as expected
atoms = formula('SiO2').atoms
rho,mu = xray_sld(atoms,density=2.2,energy=xray_energy(Cu.K_alpha))
assert_almost_equal(rho, 18.87, 2)
atoms = formula('B4C').atoms
rho,mu = xray_sld(atoms,density=2.52,energy=xray_energy(Cu.K_alpha))
assert_almost_equal(rho, 20.17, 2)
F = formula('', density=0)
rho,mu = xray_sld('', density=0, wavelength=Cu.K_alpha)
assert rho==mu==0
# Check natural density calculations
D2O_density = (2*D.mass + O.mass)/(2*H.mass + O.mass)
rho,mu = xray_sld('D2O',natural_density=1,wavelength=1.54)
rho2,mu2 = xray_sld('D2O',density=D2O_density,wavelength=1.54)
assert_almost_equal(rho, rho2, 14)
assert_almost_equal(mu, mu2, 14)
# Check f0 calculation for scalar, vector, array and empty
Q1,Q2 = 4*pi/Cu.K_alpha, 4*pi/Mo.K_alpha
f0 = Ni.xray.f0(Q=Q1)
assert_almost_equal(f0, 10.11303, 5)
assert isnan(Ni.xray.f0(Q=7*4*pi))
f0 = Ni.xray.f0(Q=Q1)
m0 = Ni.xray.f0(Q=Q2)
B0 = Ni.xray.f0(Q=[Q1,Q2])
assert (B0==[f0,m0]).all()
f0 = Ni.xray.f0(Q=[])
assert len(f0) == 0
f0 = Ni.xray.f0(Q=[[1,2],[3,4]])
assert abs(f0[0,0] - Ni.xray.f0(1)) < 1e-14
assert abs(f0[0,1] - Ni.xray.f0(2)) < 1e-14
assert abs(f0[1,0] - Ni.xray.f0(3)) < 1e-14
assert abs(f0[1,1] - Ni.xray.f0(4)) < 1e-14
# Check f0 calculation for ion
Ni_2p_f0 = Ni.ion[2].xray.f0(Q=Q1)
assert abs(Ni_2p_f0-10.09535) < 0.00001
Ni58_2p_f0 = Ni[58].ion[2].xray.f0(Q=Q1)
assert Ni_2p_f0 == Ni58_2p_f0
# The following test is implementation specific, and is not guaranteed
# to succeed if the extension interface changes.
assert '_xray' not in Ni[58].__dict__
def test_refl():
from io import StringIO
# http://henke.lbl.gov/optical_constants/mirror2.html
data2=StringIO("""\
#SiO2 Rho=2.2, Sig=3.nm, P=1., 2.deg
# Photon Energy (eV), Reflectivity
30.0000 0.900114
42.6000 0.894588
60.4919 0.888959
85.8984 0.867922
121.976 0.724582
173.205 0.742043
245.951 0.752193
349.250 0.752260
495.934 0.717134
704.226 0.392855
1000.00 5.563799E-02""")
data3=StringIO("""\
#SiO2 Rho=2.2, Sig=3.nm, P=1., 3.deg
# Photon Energy (eV), Reflectivity
30.0000 0.853800
42.6000 0.845758
60.4919 0.837342
85.8984 0.806430
121.976 0.611468
173.205 0.630653
245.951 0.633574
349.250 0.604126
495.934 0.317861
704.226 2.655170E-02
1000.00 1.240138E-03""")
e, R2 = np.loadtxt(data2).T
e, R3 = np.loadtxt(data3).T
R = mirror_reflectivity(
energy=e*1e-3, angle=[2,3],
compound='SiO2', density=2.2, roughness=30)
assert np.max(abs((R-np.vstack([R2,R3]))/R)) < 2e-4
def main():
test_xsf()
test_refl()
if __name__ == "__main__": main()
|
