XPS

Average Matrix Relative Sensitivity Factors (AMRSFs) for X-ray Photoelectron Spectroscopy (XPS) These tables and plots contain AMRSFs for XPS calculated for the total peak area for all core levels with greater than 17 eV binding energy for both Mg and Al Kα X-rays for instruments operated at the magic angle where, classically the effect of the dipole anisotropy parameter, β, is removed. At the magic angle, the angle between the incident photon beam and the detected photoelectrons is 54.7º. The background to, and use of, AMRSFs, I iAv , is discussed by Seah, Gilmore and Spencer [1] and also in ISO 18118 [2]. For homogeneous solids, the atomic fraction of element A, XA, is given by XA =

I Am / I AAv ∑ I im / I iAv

(1)

i

where the Iim are the measured peak area intensities for the element i in the sample m. These AMRSFs are based on theory and are thus for use with spectrometers for which the intensity/energy response function is calibrated [3] or otherwise known [4]. They are unlikely to be as accurate, for quantification, as properly determined experimental sensitivity factors, measured on the instrument with the correct settings for which they are intended to be used [2]. It should be noted that these AMRSFs are thought to be valid for all systems, irrespective of the chemical state, but are only valid for a correct measure of the peak areas. The most correct general background to remove for homogeneous solids is Tougaard's background [5]. It is very common to use Shirley's background [6] but this does not give intensities that either agree with Tougaard's background or with theory [7] These AMRSFs are not for use with Shirley's background. The calculations of the AMRSFs use the procedure of Seah, Gilmore and Spencer [1] in which the AMRSFs, for the core level X in the element A, are given by: Av I AX = n AXi σ AX i (hv) N Av QAv λ Av ( E AXi )

(2)

where nAXi is the population of the level Xi, σ AX i (hv) is photoionisation cross section for

each electron in the core level Xi in the element A for X-ray photoelectrons of energy hν, NAv is the atomic density of the average matrix, QAv is a term allowing for the reduction in overall escape probability of electrons from the average solid arising from elastic scattering, λAv(EAX) is the inelastic mean free path (IMFP) for the Auger electrons with average energy EAXi in the average matrix. The contributions of NAv, QAv and λAv(EAX) are discussed in the document for AES AMRSFs and are the same here. The photoelectron cross sections used here are those of Scofield which have been found to be in good agreement with measurements.

© Crown copyright 2006

Page 1 of 14 pages Page 1 of 10

XPSAMRSFsweb.doc Version 1 (29/9/06)

The calculated results are given in Tables I and II for Mg and Al X-rays, respectively, as shown in Figure 1(a) and (b). Tables III and IV show the AMRSFs ratioed to C as unity. These data are slightly different from those published in reference [1] where, for comparison with experiment, a secα term was included in equation (1) and, in the plots there, often adjacent peaks were combined. For work at angles, γ, between the incident X-rays and the detected photo-emitted electrons, other than the magic angle, an angular anisotropy needs to be considered. For homogeneous solids within the dipole approximation, the angular distribution is given by an added factor, G(γ), on the right of Eq. (2) where, for angles of emission less than 60º from the surface normal [8], GA (γ ) = 1 + 12 (0.69 β AXi ) ( 32 sin 2 γ − 1)

(3)

where β AXi is the angular anisotropy parameter for the level Xi in the element A. Equation (3) includes the effects of elastic scattering in the 0.69 appropriate for the average matrix. Figure 2 shows how this term affects the intensities for scattering angles, g, in the range 45º to 90º. For scattering angles in the range 90º to 180º, use 180º – γ. In Fig 2, the β values are from 0.5 to 2. For all s levels, β = 2. For the other angles, the values are taken from Reilman et al [9]. These are given at intervals of 5 in Z and so a simple linear interpolation has been used for the plots of b for relevant levels for Mg and Al Kα X-rays in Figs. 3 (a) and (b), respectively. For angles other than the magic angle, the effects of Figs 2 and 3 need to be included.




0.01 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 0.001

3d3/2 3d5/2

AMRSF

4s 4p1/2 4p3/2 4d3/2 4d5/2 4f5/2

0.0001

4f7/2 5s 5p1/2 5p3/2 5d3/2 5d5/2 6s 0.00001 0

10

20

30

40

50

60

70

80

90

Z

(a) Mg Kα X-rays 0.01 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 0.001

3d3/2 3d5/2

AMRSF

4s 4p1/2 4p3/2 4d3/2 4d5/2 4f5/2

0.0001

4f7/2 5s 5p1/2 5p3/2 5d3/2 5d5/2 6s 0.00001 0

10

20

30

40

50

60

70

80

90

Z

(b) Al Kα X-rays Figure 1 - The AMRSFs for all core levels with binding energies greater than 17 eV for Mg and Al Kα X-rays.




1.4 β = 0.5 0.75 1 1.25 1.5 1.75 2

1.3

G(γ )

1.2

1.1

1

0.9

0.8 45

50

55

60

65

70

75

80

85

90

angle γ

Figure 2 – Dependence of G(γ) on γ for 0.5 ≤ β ≤ 2.




2 2p 3p 3d 4p 4d 4f 5p 5d

β

1.5

1

0.5

0 0

10

20

30

40

50

60

70

80

90

50

60

70

80

90

Z

(a) Mg Kα X-rays

2 2p 3p 3d 4p 4d 4f 5p 5d

β

1.5

1

0.5

0 0

10

20

30

40 Z

(b) Al Kα X-rays Figure 3 – Values of β as a function of Z for relevant core levels for (a) Mg and (b) Al, Kα X-rays.

[1] [2]

M P Seah, I S Gilmore and S J Spencer, J. Electron Spectrosc. 120 93-111 (2001). ISO 18118:2004 - Surface chemical analysis - Auger electron spectroscopy and X-ray photoelectron spectroscopy - Guide to the use of experimentally determined relative




[3] [4] [5] [6] [7] [8] [9]

sensitivity factors for the quantitative analysis of homogeneous materials, ISO, Geneva (see also S Tanuma, Surface and Interface Analysis 38 178-180 (2006)). http://www.npl.co.uk/nanoanalysis/a1calib.html. M P Seah, J. Electron Spectrosc. 71 191-204 (1995). S Tougaard, Surface and Interface Analysis 11, 453-472 (1988). D A Shirley, Phys. Rev. B 5, 4709 (1972). M P Seah and I S Gilmore, Phys. Rev. B 73 174113 (2006) M P Seah, Surface Analysis by Auger and X-Ray Photoelectron Spectroscopy, Eds D Briggs and J T Grant, SurfaceSpectra Ltd/I M Publications 2003, pp 345-375, Chapter 13, Quantification in AES and XPS. R F Reilman, A Msezane and S T Manson, J. Electron Spectrosc. 8 389-394 (1976).




Table I – Calculated AMRSFs for Mg X-rays Level Z=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

2p1/2

2p3/2

3s

0.000115 0.000152 0.000193 0.000237 0.000283 0.000328 0.000376

0.0000214 0.0000359 0.0000565 0.0000838 0.000118 0.000162 0.000214

0.0000422 0.0000708 0.000111 0.000164 0.000232 0.000316 0.000418

0.0000397 0.0000494

0.000454 0.000488 0.000512 0.000531 0.000541 0.000542 0.000528 0.000498 0.000457 0.000405

0.000341 0.000415 0.000495 0.000581 0.000665 0.000749 0.000819 0.000880 0.000918 0.000925 0.000905 0.000826

0.000666 0.000810 0.000966 0.00113 0.00130 0.00147 0.00161 0.00174 0.00182 0.00185 0.00183 0.00170

1s

2s

0.0000175 0.0000569 0.000133 0.000251 0.000404 0.000575 0.000723

0.0000405 0.0000596

3p1/2

3p3/2

3d3/2

3d5/2

4s

0.0000746 0.0000908 0.000105 0.000120 0.000135 0.000149 0.000167 0.000183 0.000199 0.000214 0.000228 0.000244 0.000261 0.000277 0.000294 0.000309 0.000323

0.0000369 0.0000510 0.0000647 0.0000802 0.0000974 0.000114 0.000136 0.000158 0.000181 0.000205 0.000227 0.000255 0.000284 0.000313 0.000345 0.000375 0.000405

0.0000720 0.0000993 0.000126 0.000156 0.000189 0.000220 0.000265 0.000307 0.000351 0.000398 0.000438 0.000492 0.000550 0.000608 0.000670 0.000729 0.000792

0.000147 0.000190 0.000239 0.000295 0.000363

0.000214 0.000276 0.000349 0.000431 0.000527

0.0000344 0.0000404 0.0000468

0.000349 0.000360 0.000370 0.000378 0.000384 0.000392

0.000463 0.000487 0.000511 0.000536 0.000556 0.000575

0.000905 0.000961 0.00101 0.00107 0.00111 0.00116

0.000515 0.000602 0.000700 0.000805 0.000918 0.00104

0.000749 0.000881 0.00102 0.00118 0.00134 0.00151

0.000395 0.000391 0.000387 0.000379 0.000363 0.000345 0.000320 0.000292 0.000261

0.000601 0.000608 0.000612 0.000608 0.000600 0.000583 0.000559 0.000528 0.000490 0.000447

0.00123 0.00125 0.00128 0.00129 0.00128 0.00127 0.00124 0.00120 0.00115 0.00107

0.00130 0.00144 0.00158 0.00172 0.00186 0.00199 0.00211 0.00223 0.00233 0.00241

0.000892

0.00250 0.00248 0.00245 0.00240 0.00234 0.00225


4p1/2

4p3/2

0.0000628 0.0000723 0.0000811 0.0000903 0.0000982 0.000107

0.0000695 0.0000807 0.0000922 0.000102 0.000113

0.000134 0.000157 0.000179 0.000198 0.000221

0.00189 0.00209 0.00230 0.00251 0.00271 0.00291 0.00309 0.00327 0.00342 0.00355

0.000125 0.000134 0.000143 0.000153 0.000163 0.000173 0.000183 0.000193 0.000203 0.000212

0.000137 0.000149 0.000159 0.000172 0.000186 0.000201 0.000215 0.000229 0.000244 0.000258

0.00369 0.00369 0.00365 0.00361 0.00354 0.00344

0.000230 0.000238 0.000247 0.000250 0.000257 0.000262 0.000273 0.000276 0.000280 0.000279 0.000281 0.000281 0.000282 0.000280 0.000278 0.000277 0.000273 0.000269 0.000262 0.000257 0.000250 0.000241 0.000233 0.000223 0.000210 0.000197 0.000181 0.000165

5s

5p1/2

5p3/2

0.000839 0.000924 0.00101 0.00107 0.00114 0.00121

0.0000459 0.0000518 0.0000579 0.0000565 0.0000585 0.0000603

0.0000545 0.0000562 0.0000579

0.000110 0.000114 0.000118

0.00136 0.00143 0.00151 0.00156 0.00162 0.00169 0.00175 0.00180 0.00185 0.00192 0.00197 0.00202 0.00207 0.00213 0.00218 0.00222 0.00226 0.00230 0.00232 0.00233 0.00234 0.00234

0.0000636 0.0000657 0.0000703 0.0000680 0.0000682 0.0000702 0.0000707 0.0000722 0.0000730 0.0000770 0.0000810 0.0000851 0.0000891 0.0000934 0.0000977 0.000101 0.000105 0.000109 0.000112 0.000116 0.000119 0.000123

0.0000607 0.0000618 0.0000673 0.0000635 0.0000644 0.0000652 0.0000658 0.0000659 0.0000669 0.0000712 0.0000756 0.0000797 0.0000840 0.0000889 0.0000926 0.0000952 0.0000998 0.000103 0.000107 0.000110 0.000114 0.000117

0.000124 0.000127 0.000140 0.000132 0.000135 0.000138 0.000139 0.000141 0.000144 0.000156 0.000169 0.000181 0.000195 0.000209 0.000221 0.000229 0.000245 0.000259 0.000276 0.000291 0.000307 0.000326

4d3/2

4d5/2

0.000268 0.000291 0.000314 0.000337 0.000369 0.000399 0.000428 0.000459 0.000493 0.000526

0.000316 0.000366 0.000418 0.000468

0.000455 0.000528 0.000600 0.000679

0.000281 0.000293 0.000307 0.000311 0.000321 0.000329

0.000583 0.000614 0.000647 0.000663 0.000687 0.000713

0.000579 0.000637 0.000700 0.000735 0.000788 0.000840

0.000342 0.000344 0.000353 0.000352 0.000351 0.000352 0.000350 0.000347 0.000346 0.000344 0.000338 0.000332 0.000325 0.000317 0.000308 0.000298 0.000286 0.000273 0.000261 0.000243 0.000224 0.000208

0.000752 0.000773 0.000795 0.000806 0.000824 0.000837 0.000850 0.000858 0.000872 0.000882 0.000890 0.000894 0.000900 0.000907 0.000910 0.000909 0.000909 0.000905 0.000900 0.000882 0.000867 0.000849

0.000937 0.000985 0.00104 0.00108 0.00112 0.00116 0.00120 0.00124 0.00127 0.00131 0.00134 0.00137 0.00141 0.00144 0.00147 0.00149 0.00151 0.00153 0.00154 0.00154 0.00154 0.00153

Page 7 of 10

4f5/2

0.00106 0.00120 0.00135 0.00151 0.00168 0.00185 0.00203 0.00222 0.00242 0.00261 0.00280 0.00301

4f7/2

0.00135 0.00153 0.00172 0.00193 0.00214 0.00236 0.00260 0.00284 0.00309 0.00333 0.00359 0.00385

5d1/2

5d3/2

0.000272 0.000300

0.000389 0.000434

Version 1 (29/9/06)

Table II – Calculated AMRSFs for Al X-rays Level Z=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

2p1/2

2p3/2

3s

0.0000872 0.000117 0.000151 0.000188 0.000227 0.000269 0.000309

0.0000138 0.0000234 0.0000372 0.0000559 0.0000802 0.000111 0.000148

0.0000271 0.0000460 0.0000732 0.000110 0.000157 0.000217 0.000289

0.0000392

0.000387 0.000423 0.000454 0.000481 0.000502 0.000517 0.000520 0.000518 0.000502 0.000475 0.000437 0.000383

0.000243 0.000299 0.000363 0.000432 0.000505 0.000581 0.000652 0.000723 0.000784 0.000832 0.000863 0.000856 0.000817

0.000472 0.000583 0.000706 0.000842 0.000984 0.00113 0.00127 0.00141 0.00154 0.00164 0.00171 0.00171 0.00166 0.00152

1s

2s

0.0000118 0.0000392 0.0000936 0.000181 0.000302 0.000446 0.000591

0.0000297 0.0000442

0.000711

3p1/2

3p3/2

3d3/2

3d5/2

4s

0.0000601 0.0000733 0.0000854 0.0000979 0.000111 0.000122 0.000138 0.000152 0.000166 0.000179 0.000192 0.000206 0.000221 0.000238 0.000252 0.000268 0.000282

0.0000260 0.0000363 0.0000465 0.0000580 0.0000711 0.0000836 0.000101 0.000118 0.000137 0.000156 0.000174 0.000198 0.000222 0.000247 0.000274 0.000302 0.000331

0.0000506 0.0000707 0.0000902 0.000113 0.000138 0.000162 0.000195 0.000229 0.000263 0.000301 0.000335 0.000380 0.000427 0.000478 0.000531 0.000583 0.000640

0.0000937 0.000122 0.000155 0.000194 0.000239

0.000136 0.000177 0.000226 0.000282 0.000346

0.0000287 0.0000339 0.0000393

0.000310 0.000322 0.000334 0.000345 0.000355 0.000364

0.000384 0.000409 0.000435 0.000460 0.000484 0.000507

0.000747 0.000800 0.000853 0.000905 0.000952 0.00100

0.000346 0.000409 0.000478 0.000554 0.000637 0.000728

0.000502 0.000594 0.000694 0.000807 0.000927 0.00106

0.000375 0.000380 0.000380 0.000379 0.000374 0.000366 0.000353 0.000338 0.000319 0.000294

0.000544 0.000559 0.000570 0.000579 0.000581 0.000578 0.000571 0.000560 0.000542 0.000518

0.00109 0.00113 0.00116 0.00119 0.00121 0.00121 0.00121 0.00121 0.00119 0.00116

0.000926 0.00103 0.00115 0.00126 0.00138 0.00149 0.00161 0.00172 0.00183 0.00193

0.000235

0.000446 0.000404 0.000360

0.00106 0.000992 0.000924 0.000847 0.000769


4p1/2

4p3/2

0.0000529 0.0000610 0.0000687 0.0000764 0.0000833 0.0000910

0.0000561 0.0000656 0.0000752 0.0000836 0.0000934

0.000108 0.000126 0.000145 0.000161 0.000181

0.00135 0.00150 0.00166 0.00183 0.00200 0.00217 0.00234 0.00250 0.00266 0.00281

0.000107 0.000115 0.000122 0.000131 0.000140 0.000148 0.000158 0.000167 0.000176 0.000185

0.000114 0.000124 0.000133 0.000145 0.000157 0.000170 0.000183 0.000196 0.000209 0.000222

0.00209 0.00214 0.00220 0.00224 0.00226 0.00226

0.00305 0.00314 0.00324 0.00331 0.00336 0.00339

0.000203 0.000209 0.000218 0.000224 0.000229 0.000236

0.00220 0.00213 0.00202

0.00332 0.00326 0.00313 0.00294

0.000247 0.000252 0.000258 0.000259 0.000262 0.000263 0.000266 0.000266 0.000268 0.000269 0.000266 0.000265 0.000262 0.000259 0.000255 0.000250 0.000245 0.000239 0.000231 0.000221 0.000210 0.000199

5p1/2

5p3/2

0.000636 0.000705 0.000780 0.000824 0.000887 0.000951

0.0000389 0.0000440 0.0000492 0.0000482 0.0000499 0.0000518

0.0000468 0.0000484 0.0000499

0.0000929 0.0000964 0.0000998

0.00108 0.00114 0.00122 0.00126 0.00132 0.00138 0.00144 0.00150 0.00156 0.00162 0.00168 0.00174 0.00179 0.00185 0.00192 0.00197 0.00202 0.00206 0.00210 0.00214 0.00217 0.00219

0.0000547 0.0000564 0.0000604 0.0000589 0.0000593 0.0000610 0.0000617 0.0000630 0.0000640 0.0000676 0.0000711 0.0000747 0.0000786 0.0000822 0.0000863 0.0000890 0.0000929 0.0000966 0.000100 0.000103 0.000107 0.000110

0.0000527 0.0000539 0.0000590 0.0000559 0.0000569 0.0000580 0.0000583 0.0000591 0.0000600 0.0000641 0.0000681 0.0000722 0.0000766 0.0000808 0.0000846 0.0000873 0.0000917 0.0000953 0.0000989 0.000102 0.000106 0.000110

0.000106 0.000109 0.000120 0.000114 0.000116 0.000119 0.000120 0.000123 0.000125 0.000136 0.000147 0.000158 0.000170 0.000182 0.000194 0.000201 0.000216 0.000229 0.000243 0.000257 0.000272 0.000287

4d5/2

0.000219 0.000240 0.000258 0.000281 0.000307 0.000332 0.000361 0.000387 0.000417 0.000446

0.000234 0.000271 0.000312 0.000352

0.000336 0.000389 0.000448 0.000508

0.000247 0.000257 0.000270 0.000277 0.000286 0.000296

0.000501 0.000528 0.000559 0.000577 0.000600 0.000624

0.000441 0.000488 0.000541 0.000572 0.000617 0.000660

0.000312 0.000318 0.000326 0.000328 0.000331 0.000333 0.000335 0.000336 0.000337 0.000338 0.000337 0.000333 0.000330 0.000326 0.000320 0.000314 0.000306 0.000297 0.000288 0.000275 0.000262 0.000249

0.000667 0.000687 0.000710 0.000723 0.000744 0.000758 0.000775 0.000786 0.000803 0.000819 0.000831 0.000840 0.000851 0.000862 0.000871 0.000876 0.000882 0.000887 0.000891 0.000884 0.000877 0.000765

0.000749 0.000793 0.000844 0.000880 0.000921 0.000962 0.000999 0.00104 0.00107 0.00112 0.00116 0.00119 0.00123 0.00127 0.00131 0.00134 0.00137 0.00140 0.00142 0.00144 0.00145 0.000822

Page 8 of 10

4f7/2

5s

4d3/2

4f5/2

0.000704 0.000802 0.000906 0.00102 0.00114 0.00127 0.00140 0.00154 0.00168 0.00183 0.00198 0.00214

0.000890 0.00102 0.00115 0.00130 0.00145 0.00161 0.00178 0.00196 0.00214 0.00233 0.00252 0.00272

5d1/2

5d3/2

0.000235 0.000261

0.000334 0.000372

Version 1 (29/9/06)

Table III – Calculated AMRSFs ratioed to C as unity for Mg X-rays Level Z=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

1s

2s

0.0697 0.226 0.528 1.00 1.61 2.29 2.87

0.161 0.237

2p1/2

2p3/2

0.456 0.603 0.768 0.944 1.13 1.30 1.50

0.0852 0.143 0.225 0.333 0.471 0.644 0.851

0.168 0.282 0.441 0.654 0.925 1.26 1.66

1.81 1.94 2.04 2.11 2.15 2.15 2.10 1.98 1.82 1.61

1.36 1.65 1.97 2.31 2.65 2.98 3.26 3.50 3.65 3.68 3.60 3.29

2.65 3.22 3.84 4.51 5.18 5.83 6.41 6.91 7.26 7.35 7.28 6.77

3s

3p1/2

3p3/2

3d3/2

3d5/2

4s

4p1/2

4p3/2

4d3/2

4d5/2

4f5/2

4f7/2

5s

5p1/2

5p3/2

5d1/2

5d3/2

0.158 0.196 0.297 0.361 0.419 0.478 0.539 0.593 0.663 0.727 0.791 0.853 0.907 0.973 1.04 1.10 1.17 1.23 1.29

0.147 0.203 0.258 0.319 0.387 0.453 0.543 0.629 0.722 0.817 0.905 1.02 1.13 1.24 1.37 1.49 1.61

0.286 0.395 0.501 0.620 0.752 0.877 1.05 1.22 1.39 1.58 1.74 1.96 2.19 2.42 2.67 2.90 3.15

0.584 0.754 0.951 1.17 1.44

0.852 1.10 1.39 1.71 2.10

0.137 0.161 0.186

1.39 1.43 1.47 1.50 1.53 1.56

1.84 1.94 2.03 2.13 2.21 2.29

3.60 3.82 4.04 4.24 4.42 4.60

2.05 2.40 2.78 3.20 3.65 4.13

2.98 3.50 4.06 4.68 5.32 6.02

0.250 0.288 0.323 0.359 0.391 0.426

0.276 0.321 0.367 0.405 0.451

0.535 0.624 0.712 0.787 0.880

1.57 1.56 1.54 1.51 1.45 1.37 1.27 1.16 1.04

2.39 2.42 2.43 2.42 2.39 2.32 2.22 2.10 1.95 1.78

4.89 4.99 5.08 5.11 5.10 5.04 4.93 4.76 4.56 4.27

5.17 5.71 6.29 6.85 7.40 7.92 8.41 8.88 9.29 9.60

7.54 8.33 9.16 9.99 10.8 11.6 12.3 13.0 13.6 14.1

0.498 0.535 0.569 0.608 0.648 0.687 0.727 0.767 0.807 0.844

0.545 0.592 0.634 0.685 0.742 0.798 0.854 0.913 0.970 1.03

1.06 1.16 1.25 1.34 1.47 1.59 1.70 1.83 1.96 2.09

1.26 1.46 1.66 1.86

1.81 2.10 2.39 2.70

3.55

9.93 9.88 9.73 9.56 9.30 8.94

14.7 14.7 14.5 14.3 14.1 13.7

0.913 0.946 0.981 0.995 1.02 1.04

1.12 1.17 1.22 1.24 1.28 1.31

2.32 2.44 2.57 2.64 2.73 2.84

2.30 2.53 2.79 2.92 3.13 3.34

3.34 3.68 4.03 4.24 4.54 4.83

0.183 0.206 0.230 0.225 0.233 0.240

0.217 0.224 0.230

0.439 0.454 0.468

1.08 1.10 1.11 1.11 1.12 1.12 1.12 1.12 1.11 1.10 1.08 1.07 1.04 1.02 0.995 0.959 0.927 0.887 0.835 0.783 0.719 0.656

1.36 1.37 1.40 1.40 1.40 1.40 1.39 1.38 1.38 1.37 1.34 1.32 1.29 1.26 1.23 1.19 1.14 1.09 1.04 0.966 0.893 0.829

2.99 3.08 3.16 3.21 3.28 3.33 3.38 3.41 3.47 3.51 3.54 3.56 3.58 3.61 3.62 3.62 3.62 3.60 3.58 3.51 3.45 3.38

3.73 3.92 4.14 4.29 4.46 4.62 4.76 4.93 5.03 5.21 5.34 5.47 5.59 5.72 5.84 5.92 6.01 6.08 6.11 6.13 6.11 6.10

5.39 5.68 6.01 6.20 6.46 6.71 6.94 7.16 7.38 7.62 7.83 8.04 8.25 8.46 8.68 8.83 8.99 9.13 9.21 9.27 9.32 9.33

0.253 0.261 0.280 0.271 0.271 0.279 0.281 0.287 0.290 0.306 0.322 0.338 0.355 0.372 0.389 0.401 0.417 0.433 0.447 0.460 0.475 0.489

0.241 0.246 0.268 0.253 0.256 0.260 0.262 0.262 0.266 0.283 0.301 0.317 0.334 0.354 0.368 0.379 0.397 0.410 0.425 0.437 0.453 0.465

0.495 0.506 0.559 0.527 0.537 0.549 0.554 0.562 0.573 0.621 0.671 0.721 0.775 0.830 0.879 0.912 0.976 1.03 1.10 1.16 1.22 1.30


Page 9 of 10

4.21 4.78 5.38 6.03 6.70 7.36 8.09 8.84 9.61 10.4 11.1 12.0

5.36 6.09 6.85 7.66 8.53 9.40 10.3 11.3 12.3 13.3 14.3 15.3

1.08 1.19

1.55 1.73

Version 1 (29/9/06)

Table IV – Calculated AMRSFs ratioed to C as unity for Al X-rays Level Z=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

1s

2s

0.0650 0.216 0.516 1.00 1.66 2.46 3.26

0.164 0.243

3.92

2p1/2

2p3/2

0.481 0.646 0.832 1.04 1.25 1.48 1.70

0.0758 0.129 0.205 0.308 0.442 0.610 0.816

0.149 0.253 0.403 0.604 0.865 1.19 1.59

2.13 2.33 2.50 2.65 2.76 2.85 2.87 2.85 2.77 2.62 2.41 2.11

1.34 1.65 2.00 2.38 2.78 3.20 3.60 3.98 4.32 4.59 4.75 4.72 4.50

2.60 3.22 3.89 4.64 5.42 6.23 7.02 7.79 8.47 9.03 9.43 9.44 9.13 8.40

3s

3p1/2

3p3/2

3d3/2

3d5/2

4s

4p1/2

4p3/2

4d3/2

4d5/2

4f5/2

4f7/2

5s

5p1/2

5p3/2

5d1/2

5d3/2

0.216 0.331 0.404 0.471 0.540 0.612 0.675 0.759 0.835 0.913 0.989 1.06 1.14 1.22 1.31 1.39 1.48 1.56

0.143 0.200 0.256 0.319 0.392 0.461 0.557 0.651 0.753 0.860 0.961 1.09 1.22 1.36 1.51 1.66 1.82

0.279 0.390 0.497 0.621 0.759 0.891 1.08 1.26 1.45 1.66 1.85 2.09 2.35 2.64 2.92 3.21 3.53

0.516 0.671 0.854 1.07 1.32

0.751 0.977 1.25 1.55 1.91

0.158 0.187 0.216

1.71 1.77 1.84 1.90 1.95 2.00

2.12 2.26 2.40 2.54 2.67 2.79

4.12 4.41 4.70 4.99 5.25 5.52

1.91 2.25 2.63 3.05 3.51 4.01

2.76 3.28 3.82 4.45 5.11 5.82

0.291 0.336 0.378 0.421 0.459 0.502

0.309 0.362 0.414 0.461 0.515

0.595 0.696 0.800 0.888 0.995

2.06 2.09 2.10 2.09 2.06 2.02 1.95 1.86 1.76 1.62

3.00 3.08 3.14 3.19 3.20 3.19 3.15 3.08 2.99 2.85

6.00 6.22 6.40 6.55 6.65 6.70 6.69 6.65 6.57 6.41

5.10 5.70 6.32 6.96 7.59 8.22 8.86 9.48 10.1 10.6

7.41 8.27 9.17 10.1 11.0 11.9 12.9 13.8 14.7 15.5

0.587 0.632 0.673 0.721 0.769 0.818 0.868 0.919 0.969 1.02

0.627 0.684 0.735 0.798 0.866 0.936 1.01 1.08 1.15 1.22

1.21 1.32 1.42 1.55 1.69 1.83 1.99 2.13 2.30 2.46

1.29 1.50 1.72 1.94

1.85 2.14 2.47 2.80

1.30

2.46 2.22 1.98

5.86 5.47 5.09 4.67 4.24

11.5 11.8 12.1 12.4 12.5 12.5

16.8 17.3 17.8 18.2 18.5 18.7

1.12 1.15 1.20 1.24 1.26 1.30

1.36 1.42 1.49 1.53 1.58 1.63

2.76 2.91 3.08 3.18 3.30 3.44

2.43 2.69 2.98 3.15 3.40 3.64

3.51 3.88 4.30 4.54 4.89 5.24

0.215 0.242 0.271 0.266 0.275 0.285

0.258 0.267 0.275

0.512 0.531 0.550

12.1 11.7 11.1

18.3 17.9 17.2 16.2

1.36 1.39 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.48 1.47 1.46 1.44 1.43 1.41 1.38 1.35 1.32 1.27 1.22 1.16 1.09

1.72 1.75 1.79 1.81 1.82 1.84 1.85 1.85 1.85 1.86 1.86 1.84 1.82 1.80 1.77 1.73 1.68 1.63 1.59 1.51 1.44 1.37

3.67 3.79 3.91 3.99 4.10 4.18 4.27 4.33 4.43 4.51 4.58 4.63 4.69 4.75 4.80 4.83 4.86 4.89 4.91 4.87 4.83 4.21

4.13 4.37 4.65 4.85 5.08 5.30 5.50 5.74 5.92 6.17 6.37 6.57 6.79 7.00 7.21 7.38 7.55 7.71 7.82 7.92 8.00 4.53

5.93 6.29 6.70 6.97 7.30 7.63 7.96 8.26 8.58 8.93 9.24 9.56 9.89 10.2 10.6 10.8 11.1 11.4 11.6 11.8 11.9 12.1

0.302 0.311 0.333 0.324 0.327 0.336 0.340 0.347 0.353 0.373 0.392 0.412 0.433 0.453 0.475 0.490 0.512 0.532 0.552 0.569 0.589 0.607

0.290 0.297 0.325 0.308 0.314 0.319 0.321 0.326 0.331 0.353 0.375 0.398 0.422 0.445 0.466 0.481 0.505 0.525 0.545 0.564 0.586 0.604

0.584 0.600 0.662 0.627 0.640 0.655 0.664 0.675 0.689 0.749 0.811 0.872 0.938 1.01 1.07 1.11 1.19 1.26 1.34 1.42 1.50 1.58


Page 10 of 10

3.88 4.42 4.99 5.63 6.30 6.97 7.71 8.48 9.28 10.1 10.9 11.8

4.91 5.61 6.34 7.15 8.00 8.88 9.81 10.8 11.8 12.8 13.9 15.0

1.29 1.44

1.84 2.05

Version 1 (29/9/06)