X-Ray Data Booklet
Section 1.6 MASS ABSORPTION COEFFICIENTS
Eric M. Gullikson
Mass absorption coefficients have been tabulated for elements Z £ 92, based on both measured values and theoretical calculations [see B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181 (1993); for updated values, see http:// www- cxro.lbl.gov/optical_constants/]. The mass absorption coefficient µ (cm2/g) is related to the transmitted intensity through a material of density r (g/cm3) and thickness d by –mrd I = I0e . (1) –1 Thus, the linear absorption coefficient is µ… (cm ) = µr. For a pure material, the mass absorption 2 coefficient is directly related to the total atomic absorption cross section sa (cm /atom) by N m = A s , (2) A a where NA is Avogadro’s number and A is the atomic weight. For a compound material, the mass absorption coefficient is obtained from the sum of the absorption cross sections of the constituent atoms by N m = A x s , (3) MW å i ai i where the molecular weight of a compound containing xi atoms of type i is MW = S i xiAi. This approximation, which neglects interactions among the atoms in the material, is generally applicable for photon energies above about 30 eV and sufficiently far from absorption edges. In Fig. 1-5, the mass absorption coefficient is plotted for 15 elements over the photon energy range 10–30,000 eV. In much of this range, the absorption coefficient is dominated by photoabsorption. However, for H, Be, C, N, and O, Compton (in-elastic) scattering is significant at the higher energies. In these cases, the total cross section is shown as a solid curve and the photoabsorption cross section as a separate dashed curve.
106 Hydrogen (H)
104
102
100
10Ð2 106 Beryllium (Be) 104 /g) 2 102 (cm µ 100
10Ð2
106 Carbon (C)
104
102
100
10Ð2 10 100 1000 10000 Photon energy (eV) Fig. 1-5. Plots of mass absorption coefficients for several elements in their natural forms. For H, Be, C, N, and O, the photoabsorption cross section is shown as a dashed curve.
6 10 Nitrogen (N)
104
102
100
10Ð2 107 Oxygen (O) 105 /g) 2 103 (cm µ 101
10Ð1 107 Aluminum (Al) 105
103
101
10Ð1 10 100 1000 10000 Photon energy (eV) Fig. 1-5. Nitrogen, oxygen and aluminium mass absorption coefficients
107 Silicon (Si) 105
103
101
10Ð1 107 Chlorine (Cl) 105 /g) 2 103 (cm µ 101
10Ð1 106 Iron (Fe)
104
102
100 10 100 1000 10000 Photon energy (eV) Fig. 1-5. Silicon, chlorine and iron mass absorption coefficients.
106 Nickel (Ni)
104
102
100 106 Copper (Cu)
104 /g) 2 (cm
µ 102
100 106 Molybdenum (Mo)
104
102
100 10 100 1000 10000 Photon energy (eV) Fig. 1-5. Nickel, copper and molybdenum mass absorption coefficients.
106 Ruthenium (Ru)
104
102
100
Tungsten (W) 105 /g) 2
3
(cm 10 µ
101
Gold (Au) 105
103
101 10 100 1000 10000 Photon energy (eV) Fig. 1-5. Ruthenium, tungsten and gold mass absorption coefficients.