SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 27, 816–824 (1999)

Extra-atomic Relaxation Energies and AugerParameters of Titanium Compounds

C. M. Woodbridge, X. J. Gu and M. A. Langell*Department of Chemistry and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588-0304,USA

A series of titanium compounds have been studied by x-ray photoelectron spectroscopy within the Augerparameter formalism. Two different titanium Auger parameters are reported, both calculated from bindingenergies resulting from photoemission from Ti 2p3=2 core-level states. Of the two values, one has beencommonly used for titanium Auger parameter analysis and involves a valence-level Auger transition(L3M2;3Mv), whereas the other is based purely on core-level transitions (L3M2;3M2;3). Both parameterscorrelate roughly with each other and with extra-atomic relaxation energies calculated from surroundingnearest-neighbor anion polarizabilities. However, the core-level-based Auger parameter shows significantlybetter correlation with predicted relaxation energy values, particularly when corrections are made for M2;3

multiplet splittings in the analysis. The ability to model extra-atomic relaxation with polarization energiessuggests that the ligand polarizabilities in titanium thin-film and powder samples may be estimated reliablyfrom Auger parameter data despite the high degree of covalent character found in many of these compounds.Copyright 1999 John Wiley & Sons, Ltd.

KEYWORDS: auger parameter; titanium; XPS; polarizability; extra-atomic relaxation

INTRODUCTION

The Auger parameter,, was proposed in the early 1970sby Wagner1,2 as a means of correcting for charging effectsobserved in x-ray photoelectron spectroscopy (XPS) ofnon-conducting compounds without the use of an internalstandard. The parameter is defined as the kinetic energydifference between a set of photoelectron and Augerelectron transitions for the element to be analyzed

˛ D KEAES�KEPE .1/

Since its proposal, there has been a volume of workdevoted to cataloging Auger parameter data for chem-ical identification purposes2 – 4 as well as for establish-ing a direct, quantifiable relationship between the Augerparameter value and the chemical environment of the ele-ment of interest2,5 – 7 and for phenomenological interpreta-tion of photoemission5,8 – 14 processes. Recent applicationsof the Auger parameter concept include the studies ofinterfaces,14,15 characterization of the chemical environ-ment in a series of substituted inorganic salts and simplecomplexes,6,7,16 – 18 studies of charge transfer phenomenain alloys19,20 and screening mechanisms in metals.21 – 23

One item of information potentially available throughthe Auger parameter formalism is the chemical natureof the surrounding ‘ligands’ or next-nearest neighbors ofa central, generally cationic, species. In the absence offinal-state effects, it can be shown24 – 26 that the difference

* Correspondence to: M. A. Langell, Department of Chemistry,University of Nebraska, Lincoln, NE 68588-0304, USA.E-mail: mlangell@unlinfo.unl.edu

Contract/grant sponsor: National Science Foundation; Contract/grandnumber: CHE-9616690.

in Auger parameters between that of an element in thesolid state, s, and that of its gas phase atom, a, can beapproximated as

˛s�a D �2RE .2/

whereRE is the extra-atomic relaxation resulting from ashift in electron density from the neighboring atoms in thesolid to the central cation induced by the formation of corehole(s) in the photoelectron/Auger process. The extra-atomic relaxation energy can, in turn, be estimated5,27 fromnext-nearest neighbor polarization effects by summing theinduced dipoles created by the presence of a core hole onthe central cation undergoing photoemission.

We report here Auger parameter analysis of a seriesof titanium compounds with a variety of crystallographicstructures and with the formal oxidation numbers of3C and 4C, which are common in solid-state titaniumcompounds. The Auger parameter used in these studiesemploys the binding energy of the Ti 2p3/2 photoemis-sion peak, which is well-suited for the measurement andis easily accessible with standard XPS surface analysissystems. Unfortunately, no ‘good’ corresponding Augertransition exists for the Auger parameter across the entireseries of titanium compounds. The L3M2,3M2,3 transition isin an appropriate range for Auger parameter analysis butundergoes multiplet splitting to yield two peaks at¾383and 387 eV.28,29 The higher kinetic energy peak occursas a sharp, distinct transition for titanium metal,30,31 butis no longer distinct from the lower kinetic energy peakupon oxidation to either Ti3C or Ti4C. Thus, accuratelylocating a peak maximum for the L3M2,3M2,3 transition isproblematic.

The L3M2,3MV transition has been used previously toprovide information on titanium carbides28 and nitrides31

both within the Auger parameter formalism and by

CCC 0142–2421/99/090816–09 $17.50 Received 18 December 1998Copyright 1999 John Wiley & Sons, Ltd. Revised 19 March 1999; Accepted 19 March 1999

AUGER PARAMETERS OF Ti COMPOUNDS 817

direct measurement of absolute L3M2,3MV kinetic ener-gies. Although this transition is in the appropriate energyrange for routine Auger analysis and is distinct fromother titanium Auger transitions, its use in determininga reliable Auger parameter is limited by the involve-ment of the 3d-based valence states. The intensity of theAuger transition decreases significantly with an increasein the titanium oxidation state as the 3d electron densitydecreases, and the transition also shows a structure thatvaries with 3d-valence state hybridization but is difficultto model in terms of two or three well-defined peaks.In addition, inclusion of the L3M2,3MV transition in theAuger parameter measurement makes it less straightfor-ward to obtain information from parameter shifts throughEqn (2), or through similar analysis, due to a breakdown inthe assumption of equivalent initial state energies relativeto those of the gas-phase ion. The relative usefulness ofall-core and valence-level Auger parameters in the char-acterization of binary titanium compounds is discussedbelow.

EXPERIMENTAL METHODS

Powder samples of TiC, TiN, TiB2, TiO2 in the rutileand anatase forms, TiP, TiS2, TiSi2, TiSe2, TiTe2, TiAl 3

and TiI4 were obtained commercially from Aesar (TiS2

99.8%, TiSe2 99.5%, TiSi2 99.5%, TiTe2 99.8%), Pfaltzand Bauer (TiB2 99%, TiSe2 99.5%, TiP 99%) or Aldrich(TiO2 anatase form 99.9%, TiO2 rutile form 99.99%, TiC98%, TiN 99%, TiI4, 98%) and were used without furtherpurification. The powdered samples were mounted on acarousel sample-holder (PHI Electronic Industries, model10-504) with double-sided adhesive tape and placed ina stainless-steel UHV chamber that has been describedpreviously.6,7 The principal contaminants were carbon andoxygen from the adhesive tapes.

X-ray photoelectron spectra of the Ti 2p3/2 and LMMregions were acquired for all samples in the pulse-count

mode using a Physical Electronics 15-225G cylindricalmirror analyzer set to a bandpass of 50 eV. The XPS andAuger spectra were generated with Mg K˛ radiation andare signal averaged for 100–200 scans with dwell times of50 ms and pulse-count step sizes of 0.1 eV. Absolute 2p3/2binding energies and Auger kinetic energies are reportedto be calibrated relative to the adventitious carbon30 signalat 284.6 eV. Survey scans of the C 1s region were run atthe beginning and end of each data set and no appreciabledrift was observed in the carbon peak positions. Errors inreported peak positions are taken6,7 to beš0.2 eV.

RESULTS

To illustrate the titanium Auger parameters used in thepresent analysis, Fig. 1 shows a typical broad-range XPSspectrum of TiO2 (rutile form) with two separate valuesof ˛ defined by the difference in the Ti 2p3/2 core-levelphotoemission and either the all-core-level L3M2,3M2,3

(˛core) or the valence-level L3M2,3MV (˛valence) Auger tran-sition, as indicated. In order to remove the dependence ofthe Auger parameter on XPS photoexcitation energy, themodified2 Auger parameter 0 has been used

a0coreD h� C ˛coreD BE.2p3/2/CKELMM (3a)

˛0valenceD h� C ˛valenceD BE.2p3/2/CKELMV (3b)

Correlation between 0core and˛0valence is shown in Fig. 2(a)for data obtained by use of Eqns (3a) and (3b), with ener-gies determined from the peak maxima of the transitionsspecified in the equations.

The application of the Auger parameter to its fulladvantage dictates a general requirement that sharp, well-resolved features from core-level states be employed inits determination. Unfortunately, there are no Auger tran-sitions that meet this requirement for all titanium com-pounds in energy ranges easily accessible to in-house XPSsystems, e.g. those using Mg or Al K˛ sources. Although

Figure 1. Broad-scale XPS spectrum of TiO2 (rutile) showing ˛core and ˛valence.

Copyright 1999 John Wiley & Sons, Ltd. Surf. Interface Anal. 27, 816–824 (1999)

818 C. M. WOODBRIDGEET AL.

Figure 2. Correlation between ˛0core and ˛0valence: (a) ˛0core determined from curve resolution (linear regression of the data gives R D 0.66);(b) ˛0core determined using peak maxima (linear regression of the data gives R D 0.76).

Figure 3. The LMM region of TiO2 (rutile), showing a doublet in the L3M2,3M2,3 region and a weaker L3M2,3MV peak.

titaniummetal30 hasa clear,sharpL3M2,3M2,3 Augertran-sition that is appropriatefor usein determininga charac-teristic Auger parameter,many of its compoundshaveoverlappingL3M2,3M2,3 multiplet features(Fig. 3) thatmakeprecise,reproduciblemeasurementof this transition

difficult. TheL3M2,3MV regionis evenmorecomplexandmorehighly variablein structuredue to the involvementof the 3d valenceband.

In order to determine the Auger parameter ˛0coremore accurately, the L3M2,3M2,3 Auger transition was

Surf. InterfaceAnal. 27, 816–824 (1999) Copyright 1999JohnWiley & Sons,Ltd.

AUGER PARAMETERS OF Ti COMPOUNDS 819

Figure 4. Curve resolution of the L3M2,3M2,3 region of TiO2 (rutile form), showing two peaks due to spin-exchange splitting betweenholes in M2,3 levels. Prior to fitting the two Gaussians to the observed data, a linear background was subtracted from the main peak.

curve-resolvedusing two Gaussian32 peaks,with least-squaresminimization to find the optimal fit33 to thedata, as shown in Fig. 4 for the rutile sample. Inthis plot, values of ˛0valence were simply obtained withL3M2,3MV peak maxima, as has been the previouspractice28,31,34 in determiningtitanium Auger parametersbecauseof thedifficulty in modelingthis complexvalenceregion. The higher kinetic energy L3M2,3M2,3 multipletpeak was used in the determinationof ˛0core and thecorrelationbetweenthis parameterand ˛0valence is shownin Fig. 2(b). In the cases of TiN, TiTe2 and TiI 4,the L3M2,3M2,3 region was curve-resolvedusing threeGaussiansto take into accountthe overlappingN KLL, 31

Te 3p1/230 and I 3p3/2,

30 which also occursin the LMMregionof theaforementionedcompounds.Thecorrelationbetween the core- and valence-levelAuger parameterincreasessomewhat upon fitting, with the R factordeterminedby linear regressionimproving marginallyfrom 0.66 to 0.76. More importantly, the correlationwith ligandpolarizability,describedbelow,alsoimprovessubstantiallyupon fitting the L3M2,3M2,3 region for thetwo multiplet states.Therefore,all ˛0core dataarereportedusingthecurve-resolvedL3M2,3M2,3 multiplet peakunlessnotedotherwise.

Absolute peak positionsof the 2p3/2, L3M2,3M2,3 andL3M2,3MV linesof thetitaniumcompoundsarereportedinTable1. For all compoundsexceptTiC, the Ti 2p3/2 peakis shifted towardhigher binding energieswith respecttometallic titanium, as appropriatefor titanium in 3C or4C oxidationstates.Whereavailable,literaturevaluesforthe Ti 2p3/2 peakandthe˛0valence Augerparameterarealsoreportedin Table1. Agreementbetweentheliterature2p3/2

peaksand thosedeterminedin this study is mixed, per-hapspartly dueto incompletecompensationfor chargingeffectsbutalsodueto thewiderangeof typesof substratesreportedas typical of the elementof interest.Severalofthe samplesare thin films and others,particularly TiN,31

TiC28 and TiO2,39 show large rangesof variation from

Table 1. Binding energiesfor Ti 2P3=2, kinetic energiesfor TiL3M2;3M2;3 L3M2;3MV lines and calculated Augerparameters

2p3/2 ˛0val

Salt 2p3/2 (Ref.) KEcore KEval ˛0core ˛0val (Ref.)

Bulk Ti 453.8 873.1(30) (34)

TiC 453.9 454.6 389.9 420.5 843.8 874.4 872.8(34) (34)455.1(28)

TiN 454.3 455.1š 0.5 386.8 418.5 841.1 872.8 875.7(36) (34)

TiP 454.3 454.8 387.9 419.5 842.2 874.2(34)

TiB2 454.4 454.3 387.8 420.3 842.2 874.7(30)

TiO2 460.1 459 382.9 418.2 843.0 873.5anatase (35)

458.8š 1.3(38)

TiO2 459.6 459 383.0 418.6 842.6 873.4 873.6rutile (35) (34)

458.8š 1.3(38)

TiS2 454.4 387.6 418.7 842.0 873.3TiSi2 454.6 456.2 388.0 419.0 842.6 873.6

(28)TiSe2 454.0 387.3 418.5 841.3 872.5TiTe2 454.3 385.9 416.8 840.2 871.1TiAl3 454.8 385.1 419.1 839.9 873.5TiI4 454.2 384.8 417.4 839.0 871.6

All energies are in eV. Numbers in parentheses are referencenumbers.

stoichiometeryand thereforevariation in literaturebind-ing energy values.Inaccuraciesin calibrationof absoluteenergies do not affect Auger parametervalues,becauseshifts in the photoelectronand Auger transitionenergiescancelin determiningthe parameter(Eqn (3)). However,

Copyright 1999JohnWiley & Sons,Ltd. Surf. InterfaceAnal. 27, 816–824 (1999)

820 C. M. WOODBRIDGEET AL.

the Auger parameters fare no better in their overall agree-ment with literature values. This discrepancy illustrates thedifficulty in using Auger parameters with valence transi-tions, which may be sensitive to small changes in surfaceconditions or otherwise difficult to assign unambiguouslydue to their broad and complicated nature.

For ease of conceptualization, the Auger parameter canbe separated10,24,25,40 into three contributions: one from theinitial-state charge distribution on the titanium; a secondfrom the internal relaxation of orbital energies within thetitanium in response to the creation of a core hole andsubsequent Auger decay processes; and a third due toexternal relaxation of the ligand orbital energies resultingin electron density transfer to the titanium during pho-toemission and subsequent Auger decay. By measuringthe Auger parameter of titanium in the compound rel-ative to that of its analogous gas-phase cation, whichpossesses the same initial-state charge distributions andinternal relaxation energies, the first two of the contri-butions will cancel, leaving only the dependence on thesurrounding ligand relaxation energiesRE (Eqn (2)). Inthe absence of final-state effects,RE can be modeled5,41,42

by the ligand polarization energy resulting in response tothe formation of the cation core hole.

A simple electrostatic model for the polarization energy5

assumes that the ligands are arranged about the centralcation and form induced dipoles,Mj, on each of thejligands in response to the applied field,F, of the cationcore hole. The induced dipole strength is related to˛P, theelectric polarizability of the ligand, such thatM D ˛PFL,whereFL is the local dipolar field on the ligand. ObtainingFL requires a vector sum ofF and FD,—the sum of theportion of FL at each ligand resulting from dipole–dipoleinteractions of theMj with each other

FL D F C FD D e

4�ε0R2C 1

4�ε0

∑j6Di

[3.Mj Ð Rij/Rij

R5ij �Mj/R3

ij

].4/

whereRij is the vector connecting ligandsi and j. Foran equidistant arrangement of ligands around the cation,the magnitude of the vectorRij is 2R cos�ij and the sumof vector quantities can be expressed as the product ofa single scalar component and a geometric factor thatdepends only upon the symmetry and ligand coordinationnumber. Therefore, the magnitude of the dipolar fieldbecomes

FD D �D˛PFL

4�ε0R3.5/

whereD is a geometrical term given by

D D∑j6Di

1C cos2 �ij8 cos3 �ij

.6/

D can be readily evaluated5,6 for tetrahedral, octahedraland cubic arrangements of ligands to give values of 1.148,2.371 and 3.996, respectively. Substituting Eqn (4) intoEqn (5) and rearranging shows thatFL D F / , where D1CD˛P/4�ε0R3, and because the extra-atomic relaxationenergy is approximated as the polarization energy,EP, ofthe surrounding ligands upon creation of a core hole onthe titanium cation

RE D EP D nF∫

0

MdF D 1

2n˛PF

2/ .7/

The Auger parameter then can be calculated relative tothe gas-phase state

˛0 D �2RE D �2[14.4 Ð 1

2Ð(n˛P

R4

)].8/

Collected constants give rise to the value of 14.4 inEqn (8) and assume that˛P is in cubic angstroms andR isin angstroms, to yield Auger parameter values in eV. If,for the reference value for˛0 (D˛s�˛a), ˛a is taken to bethe gas-phase titanium cation appropriate to the oxidationstate of the compound of interest, the in Eqn (8) canbe eliminated from the terms involving external relaxationeffects on the gas-phase ion

˛0 D �2RE D �2[14.4 Ð 1

2Ð(n˛P

R4

)].9/

Relaxation energies still can be obtained for compoundsin which the coordinating ligands are not all equidistantfrom the central cation, but for these compounds nosimple geometric constant will describe the dipolar fieldbecause theMj of Eqn (4) couple in a manner that isno longer easily averaged to a single scalar quantity.Instead, theFLj at each ligand must be separated bymatrix inversion methods, at which point the individualligand’s contribution to the relaxation energy can becalculated in a manner analogous to that used to determineEP in Eqn (7). The values are then summed over allnear-neighbor ligands to getRE. The electrostatic modelfor the case of an unsymmetrical ligand distribution isidentical to that developed for the equidistant, symmetricalligand distribution above but, by necessity, the algebra ismore complicated. The procedure is described in detail7

elsewhere.The extra-atomic relaxation energies calculated from

the electrostatic model for the titanium compounds arereported in Table 2, which also summarizes the literaturepolarizabilities43 – 46 and crystal structures35,36,47,48 used inthe calculations. Core and valence Auger parameters areplotted versus�2RE in Figs 5 and 6, respectively. Acorrelation between the Auger parameter and polarizationrelaxation energy is established for both˛0core and˛0valence,although it is clearly better for the Auger parameter usingonly core transitions. The slope of the plot, 1.0š 0.2 for˛0core and 0.7š0.2 for ˛0valence, is also in better agreement forthe core data with that predicted by Eqn (2). Not includedin the linear least-squares analyses of Figs 5 and 6 is thevalue for TiAl3, which does not follow the general trendof either plot. This is most likely due to the difficulty infinding accurate values of polarizability for the metallicalloy, which in turn yields an over-estimation of�2RE

for this compound. Figure 5 also shows the correlationbetween˛0core and�2RE for Auger parameters that werecalculated with no curve resolution of the L3M2,3M2,3

multiplet, with the kinetic energy estimated from thecombined peak maximum. Neither general correlation ofthe data nor the slope is as good as that of the curve-resolved data.

The correlation predicted by Eqn (2) is not for0

and �2RE, but for ˛0a�s and �2RE, where ‘a’ and‘s’ refer to the gas-phase reference state and the solidcompound of interest, respectively. It is strictly validonly if ˛0a is comparable among the compounds of theseries, and in the case0a can be estimated from the

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AUGER PARAMETERS OF Ti COMPOUNDS 821

Table 2. Correlation between relaxation energy and Augerparameters

˛P (A)Ligand CNcation Structure (Ref.) (Ref.) ˛0core true ˛0valence �2RE

C 6 A (47) 5.90 841.20 874.4 9.81(43,49)

N 6 A (47) 3.2 839.25 872.8 7.62(43,49)

P 6 B (48) 10.5 839.75 874.2 9.08(45)

B 12 B (48) 944 839.95 874.7 7.41(45)

O (anat.) 6 B (48) 2.4 840.50 873.5 8.14(44)

O (rut.) 6 B (48) 2.4 840.40 873.4 8.01(44)

S 6 B (48) 5.5 839.75 873.3 7.13(44)

Si 10 B (48) 55.1 839.95 873.6 8.64(45)

Se 6 B (48) 7 838.95 872.5 7.35(44)

Te 6 B (48) 9 838.50 871.1 6.92(44)

Al 4 B (48) 5118 837.65 873.5 12.92(45)

I 4 C(35,36) 6.294 837.55 871.6 5.75(46)

All energies are in eV. Numbers in parentheses are referencenumbers

intercept. Both core and valence parameters suffer fromthe problem that appropriate gas-phase reference stateshould be expected to vary within the series becausethe materials have different initial-state valence electrondensities. Although the majority of compounds studied arecomprised for formally Ti4C cations, TiN, TiP and TiAl3are formally Ti3C. Furthermore, there is a considerableamount of covalent nature to the titanium compounds andtheir formal charge is not an accurate reflection of thevalence electron density on the cation. The fact that theformally Ti4C cations in the series have multiplet effectsin their L3M2,3M2,3 Auger transition indicates that some3d character must be present in the initial or final state(s)of the Auger process because the splitting has been shownto be influenced by coupling between the M2,3 hole withthat of the 3d valence electrons.50

We justify using the same apparent gas-phase referencestate for all compounds in Fig. 5 as an approximationthat is within the variance of our measurements. Polar-ization energy calculations place values of�2RE withina relatively narrow range of energies at some distancefrom they-intercept, with most values falling between 6and 10 eV. Extrapolation down to�2RE D 0, therefore,yields a fairly high variance in the linear least-squares fitto yield a value of 834š2 eV for˛0core and 868š2 eV for˛0valence. Only a relatively small portion of the full rangeof RE that extends down to 0 eV is, therefore, gener-ally used in the Auger parameter formalism. It is believedthat˛0a for titanium ions representative of the initial-state

Figure 5. Correlation of ˛0core with relaxation energy .�2RE/: (a) curve-resolved values for ˛0core and linear regression give a slope of1.0š 0.2, an intercept of 834š 2 and an R factor of 0.87; (b) values read from peak maxima for ˛0core and linear regression give a slopeof 0.5š 0.2, an intercept of 835š 2 and an R factor of 0.59.

Copyright 1999JohnWiley & Sons,Ltd. Surf. InterfaceAnal. 27, 816–824 (1999)

822 C. M. WOODBRIDGEET AL.

Figure 6. Correlation of ˛0valence with relaxation energy .�2RE/. Linear regression gives a slope of 0.7š 0.2, an intercept of 868š 2 andan R factor of 0.73.

charge distributionfor the compoundswill lie within thistolerance. TheTi 2p3/2 bindingenergiesfor TiO2 (formallyTi4C) and Ti2O3 (formally Ti3C), for example,havepre-viously beenreportedas459.3and458.0,respectively.51

A survey51 of Ti 2p3/2 binding energies for a numberofreportedtitaniumoxidesfindsthemeanbindingenergy ofTi4C to be458.8š1.3 andTi3C to be457.0š1.4 eV. Thus,thereis a good dealof overlapin the reportedrangesofbinding energies, which suggeststhat in the compoundsstudiedthebinding energiesof Ti4C andTi3C arenot verydifferent within the uncertaintyof the presentmeasure-ments.

DISCUSSION

TheXPSanalysisof a seriesof titaniumcompoundsindi-catesthat therearecleardifferencesin thechemicalstatesof the compoundsdiscernableby Auger parameteranal-ysis. Even in caseswherethe binding energy differencesbetweenthe 2p levels of the compoundsare negligible(e.g.TiN andTiP), the Auger parameterallows the com-poundsto be distinguishedby differencesin ligand envi-ronment.In orderto evaluatethe usefulnessof the Augerparameterfor more quantitativeanalysis,we havecorre-latedtheparameterswith extra-atomicrelaxationenergiesmodeledasligandpolarizationenergiesfrom simpleelec-trostaticcalculations.The experimentaldataarefound tocorrelatewell, particularly if core-levelAuger transitions

are used in the Auger parameterformalism and effortsare madeto correct for overlapresulting from multipletsplitting.

Ideally, the Auger transition used to determine theAuger parameter should not involve valence levelsbecause rehybridization and final-state effects canintroduce shifts in valence-leveltransitions within theseries.These shifts are difficult to model and readilyviolate assumptionsmade in the development2,12 ofEqn (2). In practice,however,this is not alwaysfeasiblewith in-house XPS equipment. In the titanium metalXPS spectrum,three main LMM x-ray-excited Augertransitions30 are observed at kinetic energies 383.5,389.1 and 419.3 eV, with additional,weakerfeaturesatlower kinetic energies.30,39 The highestenergy transitioncorrespondsto the L3M2,3M4,5 (L3M2,3MV) valencelineandthemiddle transitionhasbeenassignedto L3M2,3M2,3

(3P). Thereis somediscrepancyin literatureassignmentsfor the lowestof the threetransitions,which is listed asaL2M2,3M2,3 transition,30,52 a L3M2,3M2,3 (1D) transition34,50

and a L3M1M282,3 transition in variousreports.We accept

the L3M2,3M2,3 (1D) assignmentasbeingmost consistentwith the 3P assignmentand with the expectedkineticenergiesandsplittingsbetweenthe1D and3P levels.50,53–55

The exactassignmentof the peakis not as importantasthe fact that it involvesonly core-leveltransitions.

The data presentedin Figs 5 and 6 demonstratethatthere is a clear correlationbetweenthe measuredAugerparameterand the relaxation energy calculatedusing asimple electrostaticmodel for the polarizationenergy of

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AUGER PARAMETERS OF Ti COMPOUNDS 823

the surrounding ligands.5 This may appear somewhat sur-prising in light of the high degree of covalent bondingfound in the majority of the compounds studied. Paul-ing percentage ionic character56 spans the range 10–59%.Thus, a model that considers the ligands to be polarizablespheroids of electrons with no overlapping or transferableelectron density might be anticipated to be poorly repre-sentative of the titanium compound series. However, themodel produces an acceptable correlation between Augerparameters and�2RE calculated in this way. The data pre-sented here suggest that, despite the problems with valencetransitions, 0val is a reasonable means of elucidating chem-ical information in this type of Auger parameter analysis,although a somewhat less reliable and precise correlationwill result.

The one compound that did not correlate measuredAuger parameter with extra-atomic relaxation energy isTiA3, and this extremely poor correlation is almost cer-tainly due to the severe overestimation made for the alu-minum polarizability in the TiAl3 alloy (Table 2). Whereavailable, electronic polarizabilities were obtained fromthe literature.43 – 46 However, as neither the polarizabilityof Al� nor the refractive index of TiAl3 was availablein the literature, the polarizability of Al� was estimatedusing methods outlined by Pauling.45 The same methodswere used to estimate the polarizability of neutral Al anda value of 10.32 cubic angstroms was obtained; this shiftsthe aluminide data point closer to the other data, but not

enough to include the aluminide in the least-squares analy-sis. In order to be able to include the aluminide in the dataanalysis, a better value for the polarizability of Al in TiAl3

and/or more accurate measurement of the Auger parameterneed to be obtained. Analysis of the other eleven com-pounds suggests that XPS Auger parameter measurementsprovide a quick and convenient method of determiningpolarizabilities of surface elements in thin films and pow-dered samples.

CONCLUSIONS

X-ray photoelectron spectroscopy has been used to studythe 2p region of several titanium salts. One probleminherent in Auger parameter analysis is the choice of anappropriate Auger line. Titanium is particularly difficultin that the two available Auger transitions consist of anunresolved doublet and a sharp line involving valenceelectrons. We have calculated Auger parameters usingboth Auger transitions, and both sets of data are shown tocorrelate well with extra-atomic relaxation energies.

Acknowledgements

We are grateful to the National Science Foundation for support undergrant no. CHE-9616690. We also thank Professor Gordon Gallup forhis help in developing the matrix inversion procedure used to calculateligand polarization energies.

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