Journal of Electron Spectroscopy and Related Phenomena, 14 (1978) 341-358 0 Elsevler Sclentlflc Pubhshmg Company, Amsterdam - Prmted m The Netherlands

RELATIVE DIFFERENTIAL SUBSHELL PHOTOIONISATION CROSS- SECTIONS (MgKa) FROM LITHIUM TO URANIUM

STEPHEN EVANS, ROBIN G PRITCHARD* and JOHN M THOMAS**

Edward Davies Chemrcal Laboratories, Untverslty College of Wales, Aberystwyth, Dyfed, SY23 1NE (Gt Brrtazn)

(Received 7 March 1978)

ABSTRACT

Dlfferentlal subshell photolomsatlon cross-sections, relative to Fls = 1 00, are derived from new and previously reported XPS (Mg Ka) peak intensity measurements on a mde range of compounds The data cover selected elements from LI to U, mterpolatlon procedures yield experimentally based relative cross-sectlons (< 12% on average) for at least one reasonably intense core-level signal for every element between these 1lmlt.s Comparison with calculated Hartree-Slater cross-sections, whether corrected for angular dlstrlbutlon effects or not, reveals a mean discrepancy of - 20%, well m excess of the experimental error, assessed either internally or by comparison with previous work It 1s concluded that the experlmentally based values are preferable to any calculated values avadable at present m quantitative apphcatlons of XPS Possible explanations of the dlscrepancles are dIscussed, it 1s argued that hmltatlons in the theoretical method may be an important factor

INTRODUCTION

Subshell photolomsatlon cross-sections are important m X-ray photo- electron spectroscopy (XPS) m both fundamental (physical) and applied (chemical) contexts The calculation of these quantities provides a severe test of theones of electronic structure the prmclpal current theoretical approaches have been reviewed by Burke 1 Although absolute cross-sections are also drfficult to measure rehably, the available data are sufficient to md1cat.e that, for near-threshold lornsatlon at least, it 1s often necessary to go beyond the Hartree-Fock approxlmatlon to obtam even reasonably satis- factory agreement with expelnment’ Unfortunately, however, calculations

* Present address Umlever Research Laboratorles, Port Sunlight, Wlrral, Merseyslde (Gt Britain) ** Present address Department of Physlcal Chemistry, Umverslty of Cambrldge,Lensheld Road, Cambridge, CB2 1EP (Gt Britain)

342

at these advanced levels of sophlstlcatlon have not yet been performed for most elements and the only fully comprehensive calculations reported for the usual XPS photon energes (1254 and 1487 eV) (by Scofleld2 ) em- ploy the Hartree-Slater approxnnation* While one might expect this treatment to be much better m the usual XPS energy range (well above threshold) than at lower energies, its accuracy here has not hitherto been adequately examined by expenment recent work by Bnllson and Ceasar3 has however suggested that the m’ean error IS probably ,< 25%

The practical relevance of these parameters m chemical XPS arises because most of the primary photoelectron (PE) mtenslty ongmatmg m the mter- action between one photon and one core-level 1s contamed unthm a single peak m the PE spectrum If one IS satlsfled that any vanatlon m the fraction of the total intensity which IS dlstnbuted m shakeup and shakeoff structure remains small m compason with the mtenslty of the prmclpal peak, one can relate ratios of cross-sections to the ratios of the areas under PE peaks Measurements of peak areas m PE spectra from compounds of known stolchlometry can thus be used to assess the accuracy (or, at least, the apphcablhty) of the calculated cross-sections Such measurements also have a direct pragmatic value m enabling more or less quantltatlve analyses of homogeneous solids to be made by XPS’ , and m facllltatmg the quantltatlve estlmatlon of surface coverages m surface chemical studies by PE spectro- scopy6 We have previously reported data for several subshells5p7?8 with these latter arms pnnclpally m mmd m this paper we extend the data base to cover, though somewhat less thoroughly, selected shells of the heavier elements By mterpolatlon procedures slmllar to those previously des- crlbed5*7 these measurements have enabled us to compile a table of exper- Imentally’ based relative differential subshell cross-sections which includes at least one reasonably intense PE signal for every element from hthmm to uranium, and which we expect to prove accurate to 10 12% on average m analytical apphcatlons However, the mean difference between these data and the calculated cross-sections which are avalable at present 1s as much as 20% we argue below that some of this difference must be due to assump- tions mherent m the theory, rather than to the approxlmatlon mvolved m relatmg PE peak areas to calculated subshell cross-sections The intention of this paper 1s thus both to stimulate theoretical mvestlgatlons mto the approx- imations mvolved m the calculation of cross-section ratios, and to improve slgmflcantly the quantltatlve analytical capability of XPS

EXPERIMENTAL, DATA TREATMENT, AND RESULTS

Measurements of the XPS (Mg Ka) peak mtenslty ratios exhibited by

* Earlier, closely slmllar, studies by Nefedov et al 4 were somewhat more restricted m scope

343

freshly abraded pressed-pellet samples of selected compounds m an AEI ES ZOOA electron spectrometer were made as detailed prevlously5* 7 The angle, 8, between the incident photon and the detected electron m this instrument 1s 90” Peak areas were agam determined from the dlgltally recorded spectra using a computer programme to correct for the melastlcally scattered elec- tron background, the mtenslty of which was assumed to mcrease progress- ively from the low bmdmg energy (BE) side of each peak m proportion to the total integrated peak area to lower BE5j ’

After correction for the lmears~9 increase m analyser transmlsslon mth kinetic energy (KE), these peak areas, IA,B, were used to obtam differential photolonlsatlon cross-sections (for 8 = 90”), relative to Fls = I 00 (ref IO) as m our previous studies ‘* 7 by substltutlon m the equation

IA OA . g=B

NA Ep exp (-c E;* 5 ) _- l -* N B Eg5 =p ( -cE,05)

(1)

m which NA ,* represent the number of atoms of A and B per unit volume, EA,B denote the relevant electron kmetlc enerees, and oA,B are the requued dlfferentlal photolonlsatlon cross-sections The exponential terms take account of a mean quantity of surface contammatlon as discussed pre- v1ously7 c IS an emplncally determined constant having a value (for our ex- perlmental condltlons) of - 14 3 (ref 7) The term m E* 5 allows for the varlatlon m electron escape depth with KE any deviation from this simple relation IS partly compensated m the evaluation of c, agam as previously discussed’ l7 The error attnbutable to these energydependent terms, taken together, 1s thus unlikely to exceed - 3% over the maximum energy range (850-1240 eV) used m these studies The results of this procedure are shown m Table 1, slmllar experimental results for the Is, 2s, 2p, and 3p subshells of lighter elements have been reported elsewhere5*73 * , m con- nection with electron melastlc mean free path measurements7*’ and the analytical application of XPS5

An unportant omfsslon from these data, however, 1s the 2p shell for the first-row transltlon elements because of Its high mtenslty and (relatively) low escape depth, this signal 1s often 6 the preferred momtor for changes m the electromc structure of the substrate m surface chemical mvestlgatlons by XPS Relative cross-sections for this shell cannot7 be obtained reliably from measurements on compounds, not only because of the very frequent occurrence of intense shakeup phenomena, but also because the KE- dependent uncertamtles (m particular, contammatlon effects) would become unsatlsfactonly large at such low KE During our intensity measurements7 on the 3p shell of these elements (cleaned by ion-bombardment), however, we also recorded data for the 2p 1,2, 3,2 peaks, and have used these, with 3~ cross-sectlon data derived from measurements on compounds7, to obtain

344

TABLE 1

RELATIVE CROSS-SECTIONS FROM XPS INTENSITY DATAa

Level Reference level

Compound Area ratlob Cross-sectzon

(ew 1)

Mean (S D , %)”

Ca 2p

Br 3p

Rb 3p

Cd 3p

CI 2p

s 2P Br 3~ (s v ) K 2~ Na 2p Na KLL Cl 2p

S 2P Br 3p (q v ) Br 3~ (q v ) Cl 2p F Is

CaC12 CaS04 CaBrz KBr NaBr NaBr RbCl Rba SOz, RbBr CdBrz CdClz CdF2

1 70 2 07 0 976 0 91 98 0 a4 1 97 2 17 1 34 0 30 + 0 61 0 40 + 0 84

0 76 (3131/z )

1 34 1 30 127 (7) 1 18 0 91 0 82 0 90 (8) 0 96 1 26 112 1 23 (8) 1 31 2 12 1 91 2 02 (5) 2 07 (total)

Br 3d Br 3~ (q v 1

Rb 3d

Cd 3d

Sn 3d

I 3d

Cl 2p

Br 3~ (9 v 1 S 2P Br 3~ (4 v 1 S 2P Cl 2p Cl 2p

s 2P Pb4f (qv 1 T4d ts v 1

Cd 4d

Sn 4d

I 4d

Ce 4d W4d Hg 4d

T14d

Pb 4d

Br3P(qv) S 2P Cl 2p Cl 2p

s 2P K 2~ Pb4ftqv) Na 2p Na KLL

S 2P Na 2s

S 2P 14d(qv) Hg 4f (q v 1 Br3ptqv) Cl 2p

I4d (q v 1 Br 3~ (9 v 1

PbBrz 0 97 0 73 CdBrz 0 95 0 72 TlBr 0 98 0 74 RbCl 2 20 115 RbBr 1 68 1 34 Rbz SO4 2 25 1 15 CdBrs 4 50 6 10 CdS04 7 33 5 21 CdClz 6 62 5 92 SnClz 5 70 6 01 SnS04 7 06 5 95 Pb12 0 52 7 91

HgI2 2 80 7 99 TlI 2 62 7 48 CdBrz 0 83 0 58 CdS04 1 31 0 48 CdCl* 1 13 0 52 SnClz 1 65 0 77 SnS04 2 05 0 76 KI 1 29 105 PbIz 0 196 0 96 NaI 11 3 0 77 NaI 0 95 0 88

Ce2 6304 13 3 65 1 53 Na2 WO4 7 28 (d,,,) 2 01 (total)

HgS04 3 74 2 43

HgIz 1 48 2 28 HgClz 0 375 2 29 TlBr 2 25 2 98 TlCl 3 53 3 05 Pb12 1 68 2 91 PbBrz 2 18 3 06

0 73 (1)

1 21 (9)

5 74 (8)

5 98

7 79 (4)

0 53 (10)

0 76

0 91 (13)

1 53 20

2 33 (4)

3 02

3 03 (4)

345

TABLE 1 (continued)

Level Reference level

Compound Area rotzob Cross-se&on (eqn 1)

Menn (SD ,%)’

Pb 4d Cl 2p PbClz 3 41 3 13 Th 4d F 1s mF4 3 92 4 05 4 05

w 4f Hg 4f

T14f

Pb 4f

Th 4f

U 4f

Na 2s s 2P Cl 2p 14d(qv) Br 3~ (q v 1 Cl 2p s 2p Br3p(qv) Cl 2p Cl 2p F 1s Cl 2p s 2P

Naz WO4 19 8 HgS04 9 50 HgClz 7 50 HgIz 4 02 TlBr 6 27 TlCl 9 49 PbSO,, 10 6 PbBr2 5 96 PbC12 9 86 Thc14 14 1 ThF4 26 2 uo2 Cl* 8 76 uoz so4 12 1

2 36 2 36 3 92 3 88 3 91 (1) 3 94 5 10 5 05

5 07

4 68 5 00 5 03 (7) 5 42

10 9 11 3 111

74 82

78

Hg 5d

Tl 5d

Pb 5d

U 5d

I 4d (q v 1 J%& 0 32 Htz4f (qv) H&l2 0 087 Br3p(qv) TlBr 0 a4 Cl 2p TlCl 1 30 14d(qv) TlI 0 56 Cl 2p PbC12 1 28 Br3p(qv) PbBr2 0 78 S 2P PbS04 1 52 I4d (4 v ) Pb12 0 58 Cl 2p uoz Cl2 1 52

0 28 0 30 0 29

0 58 0 59 0 55 (11) 0 49 0 59 0 55 0 55 (6) 0 56 0 51 0 79 0 79

aPrlmary standards’ (gas phase) F 1 s = 1 00, N 1s = 0 387, S 2p = 0 458, Cl 2p = 0 600 Secondary standards from refs 5 and 7 and as indicated bCorrected for stolchlometry of the compound where necessary, uncorrected for analyser transmlsslon ‘Mean experlmental S D 7% for the 16 levels with 3 or more measurements

(necessanly rather approximate) values for the 2p cross-sections. These data, together with the final mean experlmental cross-sectlons obtained m the previously reported work5 * ’ and those of Table 1 are brought together m Table 2 which thus summanses all our experunental cross-se&on measure- ments Table 2 also includes relative cross-sectlons taken from Scofleld’s compilation* , both before (oT/aTF1,) and after (oD/c&) correction for angular dlstnbutlon effects

fJD cJT (1 + P/4) -=-C-t GIS GIS

when 6 = 90* 1.5

(2)

(see Relhnan et al ” ) where /3 1s the asymmetry parameter for the level

346

TABLE2

EXPERIMENTAL RELATIVE CROSS-SECTIONS IN COMPARISON WITH CALCULATEDVALUES

Level Element Relatzve cross-sectron (% differencea from expt m parentheses)

Expt b Calc total’ Calc dlfferentrald

2s Na 0121 Mg 0157 Al 0 171 Sl 0199 S 0 248 Cl 0257 K 0375

2P

3P

1s Ll B C N 0 F

Na Mg Al Sl S Cl K Ca Tl V Cr Fe Nl cu Zn

K Ca Tl Cr Mn Fe co Nl cu Zn Br Rb Cd

0 021 0 014 (40) 0122 0 116 (5) 0 222 0235(-6) 0378 0 416(-10) 0 55 0 669(--O) 100 100 (defn )

0092(27) 0123(24) 0160(7) 0 200(-O 5) 0 293(-17) 0 347(-30) 0458(-20)

0066 0098 0156 0232 0458 0 600 121 127 149* 139* 2 Olf 2 62* 4 70* 4 70* 4 71*

0 050(28) 0 085(15) 0135(15) 0 203(13) 0409(11) 0 554(B) 0 948(24) 1204(5) 185(-22) 225(-47) 2 70(-29) 3 75(-35) 495(-5) 565(-18) 6 41(--l)

0096 0085(12) 0176 0117(40) 022 0185(17) 019 0 263(-32) 0 21 0 317(-41) 0 26 037(-35) 037 0424(-14) 044 0484(-10) 040 0 535(-29) 0 51 0606(-17) 090 1038(-14) 123 1237(-O 6) 202 243(-18)

unaffected

unaffected

0040(48) 0070(34) 0 113(32) 0173(29) 0355(25) 0487(21) 0 848(35) 1 OB(16) 168(-12 205(-38 247(-21 34(-26) 443(6) 50(-6) 562(-18)

0 075(25) 0105(50) 0167(27) 0 240(-23) 0 286(-31) 0 340(-27) 0388(-5) 0445(-l) 0496(-21) 0561(-10) 097(-7) 116(6) 225(-11)

347

TABLE 2 (continued)

Level Element Relative cross-section (% dzfferencea from expt ln paren theses)

Expt b Calc total’ Calc dzfferenttald

4d

4f

3d Br Rb

Ag Cd Sn I

Cd Sn I cs Ba Ce W

Hg Tl Pb Th

W Au

Hg Tl Pb Th U

5d Wz Tl Pb U

Mean (numerical) difference between expt and theorye

0 73 0 71 (2) 1 21 1 042 (15) 4 76 4 24 (12) 5 74 4 73 (19) 5 98 5 80 (3) 7 79 7 66 (1 7)

0 53 0 43 (22) 0 76 0 60 (23) 0 91 0 91 (0 2) 1 59 1 14 (33) 1 92 1 27 (41) 1 53 148 (3) 20 3 17 (-45) 2 33 3 85 (-49) 3 02 3 96 (-27) 3 03 4 06 (-29) 4 05 4 81 (-17)

2 36 2 41(-2) 4 07 4 10 (-0 7) 3 91 4 50 (-14) 5 07 4 93 (2 8) 5 03 5 37 (-6 5)

111 9 74 (13) 78 1103 (-34)

0 29 0 40 (- 32) 0 55 0 46 (19) 0 55 0 51 (7) 0 79 1 08 (-31)

19%

0 61 (18) 0 90 (29) 3 68 (26) 3 96 (37) 5 02 (17) 6 50 (18)

0 38 (33) 0 53 (36) 0 80 (13) 1 01 (45) 1 12 (53) 1 31(15) 2 78 (-33) 3 30 (-34) 3 38 (-11) 3 46 (-13) 3 91 (4)

2 03 (15) 3 42 (17) 3 75 (4) 4 10 (21) 4 46 (12) 7 9 (34) 8 9 (-13)

0 36 (-21) 0 41 (29) 0 46 (18) 0 95 (-18)

21%

aDeflned as 200 (oexpt - ucalc M~exe. -t- ~,a ) bFrom this work (Table 1) and refs 5, 7 and 8 ‘From Scofield’ normahsed to F Is = 1 00 d From Scofleld’ , normahsed to F 1s = 1 00, and corrected for the angular dlstrlbutlon of the photoelectrons as described m the text eOmlsslon of the data for the transitron elements does not result m any substantial change m these means the lower figure 1s reduced by shghtly more (1%) than the higher f From 3p relative crosssectlons, via relative Intensity measurements made on ion- bombarded metalhc samples’ The electron mean free path was agam assumed to follow an E* 5 law, and residual contammatlon effects (< 5%) were neglected The 2~3,~ and 2p1,2 peaks were recorded separately the ratio between these two components varied from 2 1 (Zn, Cu) to 2 6 (V)

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Ar

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Ca

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Cr

Mn

Fe

co

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cu

Zn

Ga

Ge

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624

100

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124

0150

0

174

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365

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337

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0 81

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2

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3

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3

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As

Se

Br

Kr

Rb

Sr

Y

Zr

Nb

MO

T

c R

u R

h Pd

A

g C

d In

Sn

Sb

T

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S B

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Sm

0 75

0

84

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115

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3

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4 90

5

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5 79

6

26

6 76

7

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Eu

193

Gd

198

Tb

2 00

Dy

2 03

H

o 2

07

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2 11

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m

2 15

Y

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18

LU

2

23

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2 28

T

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35

W

2 41

R

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47

OS

2 52

Ir

2

60

0 46

Pt

2

68

0 59

A

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76

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H

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85

088

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2 95

10

4 Pb

3

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119

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13

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3

29

148

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341

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3 53

16

5 Fr

3

66

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3 78

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C

3 92

18

1 T

h 4

05

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4 17

19

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2

66

2 94

3

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3

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4 36

4

77

5 25

5

64

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6

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7

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8 69

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349

4d shell

Figure 1 Logarlthmlc plots of the experimental relatwe cross-section (Table 2) for the 4d subshell against (a) 4d binding energy and (b) atomic number

concerned the factor 1 5 arises because p = 2 for all s levels. Interpolation was then undertaken, using essentially the same procedure

as m our earlier works* 7 Polynomials of the same orders as had previously been found to be the mmmtum yielding acceptable results (v1z quadratics m the logarithm of the BE and cublcs m the calculated2 cross-sectlons)5* 7 were fitted to the expenmental data Mean fitted cross-section values for every element from hthlum to uranium are @ven m Table 3

The selection of the electron BE (rather than the elemental atomic num- ber, 2) as a parameter throughout this exercise was not entirely arbitrary It 1s convenient to consider mtenslty data as a function of 2 (refs 4, 12-14), but, as Chapman and Lohr I5 had suggested that much of the cross-se&on vanatlon for a aven shell (at constant photon energy) derived from varl- atlons m the electron energy, both posslbihtles were mltlally considered For most shells, both gave acceptable results, but for the 4d shell m particular the BE approach proved greatly supenor Throughout the lanthamde senes, the 4d BE mcreases much less strongly mth 2 than elsewhere, and it was found that a 1ogarAhmlc plot of o vs BE gave a more or less strzught lme (Fig la) whereas that of IZJ vs 2 (Fig lb) contamed an obvious dlscontmulty None of the 1ogarAhmlc plots of o vs BE deviated greatly from linearity

DISCUSSION

Zomparzson with previous experrmental work In Table 4 we compare our results with all the previously reported data on

Mg Kcr peak area ratios of which we are aware (The most comprehensive previous tabulation of Mg Kar-mduced relative mtensltles 1 3 unfortunately only @ves data based on peak heights, smce peak widths vary over a con- siderable range, such data cannot easily be compared vvlth the present re- sults ) Two categones of comparison are mcluded, expelnment with previous

350

TABLE 4

COMPARISON OF THE PRESENT DATA WITH PREVIOUSLY REPORTED RELATIVE INTENSITY MEASUREMENTS FOR MG Kcya

A - Intraelemental B - Interelemental

Ra tlo % dlfferenceb Reference Raho % dzfferenceb Reference

Expt Fitted (no of cpds )” Expt F&ted (no of cpds)

2SlZP Ne Na Mg Al Al Al Sl Sl P S Cl Ar K Numerical mean

35 16 -33 -92 17 12 10 18 -1 2 22 7 52 19 44 26 18 -25 -25 22 -24 -24 18

27 18 -69 -7 3 18 (3) -6 -9 18 (3)

26 16 6 -2 7 18 (13) 41 47

3Pl3d Br Kr Y Zr Nb MO Rh

-05 -53 18 (2) 20 16 17 8 18 35 9 18 -88 18 -77 18 -06 18

B IsfNa 2s N Is/O 1s N Is/K 2p N IS/MO 3p 0 IS/B] 4d F ls/Sb 3d Na 2sJS 2p Na 2slCr 3~ Na 2sjZr 3d S as/M0 3d

Cl 2p/Ca 2p Cl 2pjRh 3d Cl !2p/Pd 3d Cl 2p/Pb 4f

K ZPJS 2~ K 2plC1 2p K 2p/I 4d

K 2P/W 4f K 2plRe 4f K 2pIPt 4f

S 2PIW 4f Pb QfjBa 4d NumerIcal mean

-129-7 18 -8 3 18 (2) 17 39 18

32 20 (8) 15 18 -31 3 18

-19 -56 18 -173-07 18

13 18 13 20 (7)

19 5 19 5 18 30 7 18 157 18

-13 4 -11 6 18 -14 8 -49 18 -3 -15 4 23

-33 6 12 12 3

10 7 22 7 12 1 -17 13 -74 -21 11 8’

18 18 18 18 18 18 21 (13)

Xe 3d/4d -18 2 16 In 3dj4d -84 19

Mean values of % dafference for A and B together 9 2% (expt , 29 comparisons),

4d/4f 11 1% (htted, 50 comparisons)

W 24 -17 9 18 (3) Pt -26 4 18 Pb -25 2 -21 6 18 (3) Pb 30 34 19

5d l4f Pb Pb Overall mean

50 -09 18 -3 7 -10 19 67 10 5c

351

aExcludmg (prmclpally) paramagnetlc first-row transItIon-metal compounds, valence shells, and comparisons mvolvmg large (3 400 eV) KE differences bDefmed as 200 (literature value - our value)/(literature value + our value), our values taken from Table 2 for left-hand column and Table 3 for right-hand column Where necessary the relative mtensltles of the components of spin-orbit split signals have been assumed to he equal to their statlstlcal weights (2 1 for p, 3 2 for d, 4 3 for f) ‘Mean of those for which experlmental data were also available IS 9 4% for A (mtra- elemental) and 10% for B dThls Table includes several categories of measurement Those by Slegbahn et al l6 relate to gas-phase relative intensity measurements, extrapolated to zero pressure, those by Barrle and StreetI’ and Powell and LarsonI to intensity measurements on elemental sohds (and Ala 03 ), those by Wagne? , Brant and Feltham2’ and Madey et al 22 to measurements on compounds essentially slmdar to those described m this work, and that by Wyatt et al 21 to the gradient of a cahbratlon graph determined from fused mixtures of salts (The gradient was constramed to pass through the orlgm ) Most of these literature determmatlons consist of measurements on one material only where more than one was used, the number of materials 1s shown m parentheses after the reference number Allowance has been made where necessary for differing analyser transmlsslon functions (T 0: E-l for Varlan IEE-15)” and for other KE-dependent effects (via eqn 1) Wagner” gives c = 35 6 for typical IEE-15 conditions

expenment, and fitted (interpolated or extrapolated) values with previous expenment. Intraelemental and mterelemental ratios are also dlstmgulshed Table 4 shows that, overall, both the experrmentally measured cross-sections and the fitted values agree with previous work to k 12%, on average, while for mtraelemental ratios our expenmental data he, on average, mthm 7% of all previously reported comparable data Consxdermg (a) that the mternal vanatlons (1 e when several different materials were used m obtaining a cross-section value) amounted on average to 7% (see Table 1, our earlier datasB7e8 showed snnllar figures), (b) that most of the ratios previously deter- mined by others were denved from measurements on one substance only, and (c) that Wagner (the author whose work 1s most extensively quoted m Table 4) considered l8 his internal reproduclblllty also to be 7%, this level of agreement is very satisfactory. It m-iphes not merely that quantitative analysis of bulk homogeneous solids by XPS (via eqn 1) 1s now possible with < 10% accuracy on average - this aspect 1s more fully discussed else- where 5 - but that relative mtenslty data can be transferred from one type of instrument to another, if due allowance IS made for the dlffermg trans- mlsslon functions of the various mstruments These results thus suggest that the reservations recently expressed by Madey et al 22 and Bnggs23 con- cemmg the mterchangeabtilty of intensity data recorded on different mstru- ments may perhaps be unduly pesslmlstlc. A higher level of accuracy than that presently achieved would seem, m prmclple, possible - urlth the m- creased quantity of data avtiable for the hghter elements we have pre- v~ously~ found the method capable of 5% accuracy - but m the absence of specific apphcatlons we have not considered the considerable investment m tnne and materials required to extend the data base to a smular extent for the heavier elements to be appropnate

expert men

K

C,,,,Mg,,F, y-yy

5 IO z 15 20

Figure 2 Semllogarlthmlc plot of the 242~ against atomic number (A A A) experimental perlmental data from this work (Table 2), Scofleld2 and Rellman et al l1

differential cross-section ratio (8 = 90’) data from Slegbahn et al M, (0 l 0) ex- (0 0 0) calculated values derived from

As Table 4 confzms, the errors involved in determmmg mtra-atomic ratios are generally less than for mterelemental ratios In Fig 2 we compare our experimental results (Table 2) for the most precisely determined (* 4%- see Table 4 and ref 5) mtraatomlc ratio, 2s/2p for 11 C 2 G 19, with data reported by Slegbahn et al l6 Although the overlap between the two sets of data 1s mn-nmal, their mutual consMency 1s clearly apparent

Cumpamon with calculated cross-sectlons Inspection of Table 2 reveals that, on average, over 69 levels mcludmg

s, p, d and f levels, the difference between experiment and relative cross- sections denved from Scofleld’s calculatlons2 amounts to some 20%, m comparison with a mean expenmental error shown m the previous section not to exceed - 12% Surpnsmgly, the agreement 1s not merely no better but is actually noticeably worse when the angular dlstnbutlon of the photo- electrons 1s taken mto account using mterpolatlons between the 0 values reported by Rellman et al.” Smce these data were calculated at essentially the same level of approxunatlon as the total cross-sections, and since a large error m p 1s required to have any substantial effect on the differential cross-sections (eqn. 2), we may neglect maccuracles m j3 m dlscussmg the ongm of this phenomenon

One possible mterpretatlon would be that elastic scattermg of the photo- electrons effectively averages-out the angular d&,nbutlon m photoemlsslon from sollds24 however, elastic scattermg 1s unhkely to be slgrnflcant m the

353

‘\ \ \

354

gas-phase measurements of Slegbahn et al. l6 for Ne and Ar Zs/Zp and, as shown above (Fig 2, Table 4), these agree well with our data The effect of the angular dlstnbutlon correction 1s to reduce the predicted peak mtenslty for p, d and f levels relative to that for s levels thus an alternative mter- pretatlon of the result could be that the Hartree+later method under- estimates the cross-section systematically (but not umversally - see Fig 3 for L # 0) Measurement of the angular dlstnbutlon of core photo-emlsslon from solids (using an mstrument mth a variable angle between source and analyser) to establish directly the magnitude of elastic scattenng effects m polycrystallme solids would thus be of considerable interest

The calculated (angle-resolved) 2s/2p ratio 1s shown m Fig 2 (above) for comparison with experiment, and m Fig 3 we show a full comparison of our expenmental data with the calculated dlfferentlal cross-sections These plots show that the large differences between theory and expenment remarked on above m connection with Table 2 are not random m character but result from systematic trends The devlatlons are not, however, easily predictable m respect of either magnitude or dlrectlon It follows that the calculated values cannot form an adequate basis for the quantltatlve apphcatlon of XPS, despite the very considerable success of the theory m accounting quahtatlvely for all the major features of the expenmental data As remarked previously 5 , such results support the expenmental measurements conducted by Carter et aLz4 rather than their optlmlstlc suggestion that the calculated cross-sections could be used to provide quantltatlve analyses accurate to 1096, the present results suggest that then procedure would yield mean accuracies of only - 2076, with errors of over 30% occurrmg m one case m four (Table 2) Other recent work 1s also consistent unth this concluslon3 In contrast, the use of the expenmentally based cross-sections of Table 3 for analytical purposes should result m errors of this magrntude only about once m every seventeen cases (Table 4) Before concludmg that the theory 1s at fault, however, we must consider whether the dlscrepancles could result from defects m the expenment or m the assumptions made m correlating expenment with theory

The trends shown m Figs 2 and 3 clearly do not anse sunply from random error, but it IS pertment to ask whether the method used for area determmatlon could be systematically responsible no method for extractmg peak areas from raw X-ray PE spectra has an adequate theoretical basls2’. Nevertheless, m practice, ratio data obtamed usmg different methods of estlmatmg the areas very rarely differ by more than lo-1576, whereas some of the dlscrepancles amount to several tnnes this figure A good ex- ample 1s the 2s/2p ratio m K (Fig. 2) for which the theoretical value 1s not far from double that obtained from expenment * Even though background

* Wagner ‘s also has recently commented on large differences between theory and ex- perlment for the 2s/2p ratlo

355

subtractlon errors may be greater for the broader peaks (some 4d signals, for example) l8 , we are satisfied that such effects are not a major factor m most cases

Systematic KE-dependent errors, such as unsuspected devlatlons from the assumed transmlsslon function, also cannot be responsible For the 1s shell, relative cross-sectlons obtamed from X-ray absorption measurements1 5 , which suffer none of the drawbacks specific to XPS, are m excellent wee- ment with our data over a 500eV KE range ** It follows that over any more lnnlted range of KE such effects may safely be neglected

Dn-ect chemical effects may also be discounted The calculations of Nefedov et al 4 have demonstrated convmcmgly that, for non-valence shells, cross-sections do not depend detectably on the charge on the atom (ion), while more subtle effects of the type reported by Ng and Hercules26 could reasonably be expected to average out when, as m this work, data from numerous compounds are considered together

Shakeup and shakeoff effects however provide an mltlally plausible explanation, although, as we shall show, it does not stand up well to closer exammatlon These processes can be regarded as one consequence of elec- tronic relaxation, which 1s neglected m the calculations It has, however, been shown2’ that within the “sudden approxlmatlon” the calculated cross-section relates to the sum of the mtensltres of all the primary electron eJection processes mduced by the incident photon Consequently, It 1s lmphclt m our attempt to correlate these calculated cross-sections w-Ah our experimental results that differences m the fraction of the signal as- sumed to be dissipated m shakeup and shakeoff processes may be neglected

Shakeoff losses m sohds are unfortunately vtiually nnposslble to quantify experimentally, as the KE of the “shaken-off” electron IS not well defined, no discrete peak results m the PE spectrum Calculatlons28 have however suggested that, for atoms, shakeup and shakeoff losses are indeed a more or less constant fraction - about 20% - of the total intensity, although for compounds the posltlon 1s less clear Experimentally, materials appear to fall mto two classes, those showmg no readily detectable shakeup (al- though close exammatlon often reveals weak structure2g ) (these mclude all

** For example, B Is/F Is, AKE 496 eV, XPS value greater than 7 5%, C Is/F Is, AKE 407 eV, XPS value less by 3 1% The fltted values (Table 3) are m even closer agreement, these figures reducing to + 4 3% and - 1 8% respectively The relative cross-section for L1 IS derived from X-ray data (0 013) 1s however m poor agreement with our experimental value (0 021) and 1s moreover much closer to the calculated value (0 014) However, this was the least intense slgnal studied m our work, and the data had the least satisfactory internal consistency (S D 29%)5 It seems likely that here (exceptionally) much of the discrepancy between theory and experiment should be attributed to experimental factors

356

the compounds of mammoup elements that we have exammed), and those showmg marked shakeup, sometimes comparable m mtenslty with the mam peak30 This latter group includes many paramagnetic transition metal complexes31 and compounds of the lanthanlde30 and actmlde3” elements. (The reasons for this have been much dlscussed m recent years, but no one account yet seems to be generally accepted ) In this work we have excluded those mater&s showing evident shakeup effects, but the posslblllty remains that undetected shakeup and shakeoff losses m excess of the expected28 - 20%, possibly dlstrlbuted over a conslderable energy range (this would greatly reduce the hkellhood of detection), may have system- atically reduced certam of the expenmentally measured cross-sections

The followmg conslderatlons, however, mllxtate against this convenient explanation Smce all the expenmental cross-sections are ultimately referred to F Is as reference, a posltlve deviation (experunent > theory) must then imply that, for the level m questlon, less intensity had been lost m multiple excltatlon processes than was the case, on average, for F 1s to attrlbute all posltlve deviations to such processes one has to accept that for F 1s (and by lmphcatlon the 1s shells of nelghbounng elements also) “satelhte” peaks have generally 50% or more of the mtenslty of the mam peak (Dependmg on whether total or dlfferentlal values are preferred, 16 or 17 of the 69 levels considered m Table 2 show posltlve deviations of 30% or more, while a further 11-17 exceed 20%). In such circumstances, some at least of the excess structure could reasonably be expected to have been detected, its apparent absence (even m extensively studled gases such as neonI ) mclmes us to discount the hypothesis as the prmclpal factor m explammg the dlscrepancles. Moreover, for those shells where “excess” (1.e. > 20%) shakeup IS known to occur, the mtenslty of the structure 1s generally30-32 a function of the valence electronic structure of the material one would not expect systematic trends of the type seen m Fig 3 to result from the operation of this mechanism The reduction m the 3~ and (3p- derived) 2p cross-sections apparent at the start of the first transltlon series (relatme to those expected from the results for lighter elements) may well, however, be a consequence of such processes but since the overall (dls) agreement with theory IS not thereby worsened, the above conslderatlons remam vahd

Purely experimental factors thus do not seem adequate to account for all the differences observed between expenmental and calculated different& cross-section ratios, and we conclude that there must be slgmflcant factor(s) which are not adequately treated m the Hartree-Slater method for the calculation of these parameters It 1s noteworthy that the discrepancies do not mcrease progressively wrth atomic number, and it would appear that correlation and relaxation effects (other than the occurrence of multl- electron excitations) are the most hkely cause, though we cannot from these expenments assess the relative slgrnflcance of such factors We can

357

suggest, however, that a treatment which enabled the accurate predlctlon of, m particular, the 2s/Zp mtenslty ratio and its variation with 2 would be a substantial advance on exlstmg methods, and that the calculation of this ratio would provide a relatively economical way of testing new theoretical methods It has the twm advantages of not relymg solely on the expenmen- tal data of one group and of not bemg mtrmslcally dependent on mter- elemental mtensity measurements

CONCLUSIONS

The use of Hartree-Slater photolomsatlon cross-sections m quantitative analytlcal estlmatlons by XPS 1s unlikely to yield mean accuracies better than -20% Some of this error may be due to experimental factors, but a sub&ant& part apparently results from approxlmatlons mherent m the theoretical treatment This conclusion 1s most obvious m relation to the 2s/2p cross-section ratio, the recalculation of which should prove useful m the mltlal evaluation of improved theoretical methods. At present, the use of experimentally based cross-section parameters (tabulated here for 3 < 2 & 92) 1s clearly preferable for analytical work, where a mean re- llablhty of - 12% can now be achieved

ACKNOWLEDGEMENTS

We thank the SRC for support, mcludmg a Research Studentship (to RGP)

REFERENCES

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32 G C Allen and P M Tucker, Chem Phys Lett , 43 (1976) 254, and refs therem