EMP Class Notes: Bulk Absorption

2.6.1. Bulk Mass Absorption Coefficient

For a multi-element material, the mass absorption coefficients at a particular wavelength are multiplied by the mass fraction each element and summed to yield a bulk coefficient:

Bulk mass absorption coefficients decrease with increasing energy (Table 3). Mass absorption coefficients for all elements (energies from 1 keV to 20 MeV!) are available at: http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html. A technical presentation of mass absorption coefficients is available at: http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html.

Generally, more energetic radiation is absorbed less than lower energy radiation; however, higher energy radiation will be absorbed strongly if it is energetic enough to ionize another element (E > E_c). This produces "teeth" on the intensity curve (Figures 2.6.1a and 2.6.1b). These teeth are termed absorption edges. Absorption edge values for all elements are available at: http://www.bmsc.washington.edu/scatter/periodic-table.html.

MASS ABSORPTION COEFFICIENTS FOR Ka RADIATION (cm²/g)

Absorber	Emitter
Absorber	Na	Mg	Al	Si	P	S	Cl	K	Ca	Ti	Cr	Mn	Fe	Ni
O	3653	2169	1345	865	574	391	273	141	105	60	36	28	22	14
Na	562	5409	3365	2170	1444	987	691	359	266	152	92	72	57	37
Mg	768	463	4287	2768	1843	1261	883	460	341	195	118	93	74	48
Al	1019	614	386	3451	2300	1575	1104	576	427	245	148	116	93	60
Si	1319	794	499	325	2816	1929	1353	707	524	301	182	143	114	74
P	1670	1006	632	411	276	2325	1632	854	633	364	220	174	138	90
S	2076	1251	786	511	343	236	1940	1016	754	434	262	207	165	108
Cl	2542	1531	962	626	420	289	204	1194	887	511	309	244	195	127
K	3663	2207	1386	902	605	417	294	155	1188	686	415	329	262	171
Ca	4326	2606	1637	1066	715	493	347	183	136	783	475	376	300	196
Ti	5871	3571	2222	1446	970	668	471	249	185	107	607	480	384	251
Cr	7728	4655	2924	1903	1277	880	620	327	244	141	86	68	478	313
Mn	8780	5289	3323	2163	1451	1000	705	372	277	160	97	77	62	347
Fe	9918	5975	3753	2443	1639	1129	796	420	313	181	110	87	70	382
Ni	12464	7509	4717	3070	2060	1419	1001	528	393	228	138	110	88	57

As an example, consider the absorption of Ni-Ka and Co-Ka radiation in pyrite. Pyrite consists of 0.4655 Fe and 0.5345 S (weight fractions). The mass absorption coefficients are:

	Ni-Ka	Co-Ka
S	108	133
Fe	382	56

Therefore, the bulk mass absorption coefficients are:

m_Ni = 0.5345 x 108 + 0.4655 x 382 = 236
m_Co = 0.5345 x 133 + 0.4655 x 56 = 97

Notice that although Ni-Ka is more energetic than Co-Ka (7.48 keV vs. 6.91 keV), it is absorbed over twice as much because Ni-Ka radiation is sufficiently energetic to excite Fe-Ka radiation (E_c = 7.112 keV) from the pyrite. An excellent absorption calculator is available at: http://www-cxro.lbl.gov/optical_constants/atten2.html. Try entering various elements and compounds.

Figure 2.6.1a. Schematic plot of the X-ray absorption curve for a single element of high atomic weight. The qualitative features of the curve remain the same whether the vertical axis represents the probability of X-ray absorption, the stopping power of the element, or the mass absorption coefficient.

Figure 2.6.1b. Actual plot of the mass absorption coefficients of samarium for energies between 0 and 25 keV. The marked discontinuities are the absorption edges; each corresponds to a critical excitation potential in the L and M spectral series (the K absorption edge is to the right of the plotted region at 46.8 keV).