File:X-ray attenuation spectra elements mass.svg

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Summary

Description

English: X-ray mass attenuation spectra of selected elements for energies up to 250keV, linear abscissa, logarithmic ordinate.

Date

16 August 2023

Source

Own work

Author

Geek3

SVG development

The SVG code is valid.

This plot was created with Matplotlib.

Source code

Matplotlib source code

The plot was generated with Matplotlib

# -*- coding: utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate as itp
from math import *

def interp(x, max_gap=0.05):
    sections = [[x[0]]]
    # divide data into monotonic sections
    for i in range(1, len(x)):
        if x[i-1,0] < x[i,0] and x[i-1,1] >= x[i,1]:
            sections[-1].append(x[i])
        else:
            sections.append([x[i]])
    
    # interpolate within each section
    for si, s in enumerate(sections):
        if len(s) >= 2:
            # use third-order polynomial of logarithmized data
            spline = itp.make_interp_spline([log(d[0]) for d in s],
                [np.log(d[1:]) for d in s], bc_type="natural")
            
            for i in range(len(s) - 1, 0, -1):
                nsub = log(s[i-1][0] / s[i][0]) / log(1 - max_gap)
                if nsub > 1:
                    nsub = int(ceil(nsub))
                    xnew = s[i-1][0] * (s[i][0] / s[i-1][0]) ** (np.arange(1, nsub) / nsub)
                    s = s[:i] + [np.concatenate(([xnew[j]], d)) for j, d in enumerate(np.exp(spline(np.log(xnew))))] + s[i:]
        sections[si] = s
    
    return np.concatenate(sections)

# data from https://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html
mu_H = interp(np.fromstring("""
1.90000E-4 1.000E+3 1.00000E-3 7.217E+0 1.50000E-3 2.148E+0 2.00000E-3 1.059E+0
3.00000E-3 5.612E-1 4.00000E-3 4.546E-1 5.00000E-3 4.193E-1 6.00000E-3 4.042E-1
8.00000E-3 3.914E-1 1.00000E-2 3.854E-1 1.50000E-2 3.764E-1 2.00000E-2 3.695E-1
3.00000E-2 3.570E-1 4.00000E-2 3.458E-1 5.00000E-2 3.355E-1 6.00000E-2 3.260E-1
8.00000E-2 3.091E-1 1.00000E-1 2.944E-1 1.50000E-1 2.651E-1 2.00000E-1 2.429E-1
3.00000E-1 2.112E-1
""", sep=" ").reshape((-1, 2)))

mu_C = interp(np.fromstring("""
1.00000E-3 2.211E+3 1.50000E-3 7.002E+2 2.00000E-3 3.026E+2 3.00000E-3 9.033E+1
4.00000E-3 3.778E+1 5.00000E-3 1.912E+1 6.00000E-3 1.095E+1 8.00000E-3 4.576E+0
1.00000E-2 2.373E+0 1.50000E-2 8.071E-1 2.00000E-2 4.420E-1 3.00000E-2 2.562E-1
4.00000E-2 2.076E-1 5.00000E-2 1.871E-1 6.00000E-2 1.753E-1 8.00000E-2 1.610E-1
1.00000E-1 1.514E-1 1.50000E-1 1.347E-1 2.00000E-1 1.229E-1 3.00000E-1 1.066E-1
""", sep=" ").reshape((-1, 2)))

mu_N = interp(np.fromstring("""
1.00000E-3 3.311E+3 1.50000E-3 1.083E+3 2.00000E-3 4.769E+2 3.00000E-3 1.456E+2
4.00000E-3 6.166E+1 5.00000E-3 3.144E+1 6.00000E-3 1.809E+1 8.00000E-3 7.562E+0
1.00000E-2 3.879E+0 1.50000E-2 1.236E+0 2.00000E-2 6.178E-1 3.00000E-2 3.066E-1
4.00000E-2 2.288E-1 5.00000E-2 1.980E-1 6.00000E-2 1.817E-1 8.00000E-2 1.639E-1
1.00000E-1 1.529E-1 1.50000E-1 1.353E-1 2.00000E-1 1.233E-1 3.00000E-1 1.068E-1
""", sep=" ").reshape((-1, 2)))

mu_O = interp(np.fromstring("""
1.00000E-3 4.590E+3 1.50000E-3 1.549E+3 2.00000E-3 6.949E+2 3.00000E-3 2.171E+2
4.00000E-3 9.315E+1 5.00000E-3 4.790E+1 6.00000E-3 2.770E+1 8.00000E-3 1.163E+1
1.00000E-2 5.952E+0 1.50000E-2 1.836E+0 2.00000E-2 8.651E-1 3.00000E-2 3.779E-1
4.00000E-2 2.585E-1 5.00000E-2 2.132E-1 6.00000E-2 1.907E-1 8.00000E-2 1.678E-1
1.00000E-1 1.551E-1 1.50000E-1 1.361E-1 2.00000E-1 1.237E-1 3.00000E-1 1.070E-1
""", sep=" ").reshape((-1, 2)))

mu_Na = interp(np.fromstring("""
1.00000E-3 6.542E+2 1.03542E-3 5.960E+2 1.07210E-3 5.429E+2 1.07210E-3 6.435E+3
1.50000E-3 3.194E+3 2.00000E-3 1.521E+3 3.00000E-3 5.070E+2 4.00000E-3 2.261E+2
5.00000E-3 1.194E+2 6.00000E-3 7.030E+1 8.00000E-3 3.018E+1 1.00000E-2 1.557E+1
1.50000E-2 4.694E+0 2.00000E-2 2.057E+0 3.00000E-2 7.197E-1 4.00000E-2 3.969E-1
5.00000E-2 2.804E-1 6.00000E-2 2.268E-1 8.00000E-2 1.796E-1 1.00000E-1 1.585E-1
1.50000E-1 1.335E-1 2.00000E-1 1.199E-1 3.00000E-1 1.029E-1
""", sep=" ").reshape((-1, 2)))

mu_P = interp(np.fromstring("""
1.00000E-3 1.913E+3 1.50000E-3 6.547E+2 2.00000E-3 3.018E+2 2.14550E-3 2.494E+2
2.14550E-3 2.473E+3 3.00000E-3 1.118E+3 4.00000E-3 5.242E+2 5.00000E-3 2.860E+2
6.00000E-3 1.726E+2 8.00000E-3 7.660E+1 1.00000E-2 4.035E+1 1.50000E-2 1.239E+1
2.00000E-2 5.352E+0 3.00000E-2 1.700E+0 4.00000E-2 8.096E-1 5.00000E-2 4.916E-1
6.00000E-2 3.494E-1 8.00000E-2 2.324E-1 1.00000E-1 1.865E-1 1.50000E-1 1.432E-1
2.00000E-1 1.250E-1 3.00000E-1 1.055E-1
""", sep=" ").reshape((-1, 2)))

mu_Ca = interp(np.fromstring("""
1.00000E-3 4.867E+3 1.50000E-3 1.714E+3 2.00000E-3 7.999E+2 3.00000E-3 2.676E+2
4.00000E-3 1.218E+2 4.03810E-3 1.187E+2 4.03810E-3 1.023E+3 5.00000E-3 6.026E+2
6.00000E-3 3.731E+2 8.00000E-3 1.726E+2 1.00000E-2 9.341E+1 1.50000E-2 2.979E+1
2.00000E-2 1.306E+1 3.00000E-2 4.080E+0 4.00000E-2 1.830E+0 5.00000E-2 1.019E+0
6.00000E-2 6.578E-1 8.00000E-2 3.656E-1 1.00000E-1 2.571E-1 1.50000E-1 1.674E-1
2.00000E-1 1.376E-1 3.00000E-1 1.116E-1
""", sep=" ").reshape((-1, 2)))

mu_Fe = interp(np.fromstring("""
1.00000E-3 9.085E+3 1.50000E-3 3.399E+3 2.00000E-3 1.626E+3 3.00000E-3 5.576E+2
4.00000E-3 2.567E+2 5.00000E-3 1.398E+2 6.00000E-3 8.484E+1 7.11200E-3 5.319E+1
7.11200E-3 4.076E+2 8.00000E-3 3.056E+2 1.00000E-2 1.706E+2 1.50000E-2 5.708E+1
2.00000E-2 2.568E+1 3.00000E-2 8.176E+0 4.00000E-2 3.629E+0 5.00000E-2 1.958E+0
6.00000E-2 1.205E+0 8.00000E-2 5.952E-1 1.00000E-1 3.717E-1 1.50000E-1 1.964E-1
2.00000E-1 1.460E-1 3.00000E-1 1.099E-1
""", sep=" ").reshape((-1, 2)))

mu_Sn = interp(np.fromstring("""
1.00000E-3 8.157E+3 1.50000E-3 3.296E+3 2.00000E-3 1.665E+3 3.00000E-3 6.143E+2
3.92880E-3 3.114E+2 3.92880E-3 9.285E+2 4.00000E-3 9.393E+2 4.15610E-3 8.469E+2
4.15610E-3 1.145E+3 4.30764E-3 1.060E+3 4.46470E-3 9.712E+2 4.46470E-3 1.117E+3
5.00000E-3 8.471E+2 6.00000E-3 5.294E+2 8.00000E-3 2.500E+2 1.00000E-2 1.384E+2
1.50000E-2 4.664E+1 2.00000E-2 2.146E+1 2.92001E-2 7.760E+0 2.92001E-2 4.360E+1
3.00000E-2 4.121E+1 4.00000E-2 1.942E+1 5.00000E-2 1.070E+1 6.00000E-2 6.564E+0
8.00000E-2 3.029E+0 1.00000E-1 1.676E+0 1.50000E-1 6.091E-1 2.00000E-1 3.260E-1
3.00000E-1 1.639E-1
""", sep=" ").reshape((-1, 2)))

mu_Pb = interp(np.fromstring("""
1.00000E-3 5.210E+3 1.50000E-3 2.356E+3 2.00000E-3 1.285E+3 2.48400E-3 8.006E+2
2.48400E-3 1.397E+3 2.53429E-3 1.726E+3 2.58560E-3 1.944E+3 2.58560E-3 2.458E+3
3.00000E-3 1.965E+3 3.06640E-3 1.857E+3 3.06640E-3 2.146E+3 3.30130E-3 1.796E+3
3.55420E-3 1.496E+3 3.55420E-3 1.585E+3 3.69948E-3 1.442E+3 3.85070E-3 1.311E+3
3.85070E-3 1.368E+3 4.00000E-3 1.251E+3 5.00000E-3 7.304E+2 6.00000E-3 4.672E+2
8.00000E-3 2.287E+2 1.00000E-2 1.306E+2 1.30352E-2 6.701E+1 1.30352E-2 1.621E+2
1.50000E-2 1.116E+2 1.52000E-2 1.078E+2 1.52000E-2 1.485E+2 1.55269E-2 1.416E+2
1.58608E-2 1.344E+2 1.58608E-2 1.548E+2 2.00000E-2 8.636E+1 3.00000E-2 3.032E+1
4.00000E-2 1.436E+1 5.00000E-2 8.041E+0 6.00000E-2 5.021E+0 8.00000E-2 2.419E+0
8.80045E-2 1.910E+0 8.80045E-2 7.683E+0 1.00000E-1 5.549E+0 1.50000E-1 2.014E+0
2.00000E-1 9.985E-1 3.00000E-1 4.031E-1
""", sep=" ").reshape((-1, 2)))

plt.figure()
plt.plot(mu_Pb[:,0] * 1e3, mu_Pb[:,1], label="$_{82}$Pb", color="#77ac30")
plt.plot(mu_Sn[:,0] * 1e3, mu_Sn[:,1], label="$_{50}$Sn", color="#0088bd")
plt.plot(mu_Fe[:,0] * 1e3, mu_Fe[:,1], label="$_{26}$Fe", color="#d95319")
plt.plot(mu_Ca[:,0] * 1e3, mu_Ca[:,1], label="$_{20}$Ca", color="#edb120")
plt.plot(mu_P[:,0] * 1e3, mu_P[:,1], label="$_{15}$P", color="#7e2f8e")
plt.plot(mu_Na[:,0] * 1e3, mu_Na[:,1], label="$_{11}$Na", color="#555555")
plt.plot(mu_O[:,0] * 1e3, mu_O[:,1], label="$_8$O", color="#cc1122")
plt.plot(mu_N[:,0] * 1e3, mu_N[:,1], label="$_7$N", color="#5577ff")
plt.plot(mu_C[:,0] * 1e3, mu_C[:,1], label="$_6$C", color="#000000")
plt.plot(mu_H[:,0] * 1e3, mu_H[:,1], label="$_1$H", color="#aaaaaa")

plt.gca().set_yscale('log')
plt.xlim(0, 250)
plt.ylim(1e-1, 1e3)
plt.ylabel(r"$\mu/\rho$ [cm${}^2$/g]")
plt.xlabel("E [keV]")
plt.legend(borderaxespad=0.8, framealpha=1)
plt.grid()
plt.tight_layout()
plt.savefig("X-ray_attenuation_spectra_elements_mass.svg")

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	12:48, 16 August 2023		576 × 432 (62 KB)	Geek3	Uploaded own work with UploadWizard

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Mass attenuation coefficient

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- 质量衰减系数

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File:X-ray attenuation spectra elements mass.svg

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X-ray

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copyright license

Creative Commons Attribution-ShareAlike 4.0 International

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inception

16 August 2023

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