Test of a Quantitative Approach to Secondary Ion Mass Spectrometry on Glass and Silicate Standards A. E. Morgan"' and H. W. Werner Philips Research Laboratories, Eindhoven, The Netherlands
An empirical procedure to derive a sample composition from its positive, secondary ion mass spectrum has been tested on glass and silicate standards. The method belng a slngle flttlng parameter variant of other thermodynamic approaches requlres only one Internal standard. The magnitude of the flttlng parameter is about 8900 K for Ar' bombardment of these matrices in vacuum. Thls value increases (a) with oxygen bombardment or admlssion, (b) when only hlgher energy secondary ions are monitored, or (c) with an increase in the negatlve surface charging. Practlcally all elemental concentrations, Including that of oxygen, can be derived to within a factor of 2 of their quoted bulk values. Suggestions are made for improving the analytical accuracy obtainable.
In general, quantitative analyses with an accuracy of a few % are possible with secondary ion mass spectrometry (SIMS) by employing external standards for establishing calibration curves; these are often linear over several orders of magnitude of concentration (e.g., see Ref. 1 and 2). The standards should be homogeneous on a microscale and similar in composition to the analyzed material to avoid matrix effects. However, it is clearly useful to be able to circumvent this tedious, time-consuming approach if a survey (semiquantitative) analysis only is required. An example might be the estimation of impurity levels in highly-pure thin films. Further, a survey analysis often necessarily precedes the preparation of relevant references for a more accurate analysis. It is our aim to derive constituent concentrations to within a factor of two or three from a secondary ion mass spectrum of the sample. A fair degree of success was achieved with low alloy steels (3)by simply scaling the measured secondary ion currents by factors involving only one adjustable (matrixdependent) parameter, T,. In this communication we extend this method to glasses and silicates, chosen because many well-characterized specimens are available. We investigate whether T , depends significantly upon the primary ion bombarding species and energy, the residual vacuum conditions, the energy range of secondary ions monitored, and the actual sample studied. Once T,has been established, the accuracy that can be expected in compositional analyses without using standards is then examined.
BASIS FOR QUANTITATIVE ANALYSIS Several different equations proposed for the ionization ratio, nM+/nMO, can be grouped into one general expression, nM+ and nMO are the numbers of M+ ions and Mo neutrals respectively emitted per unit time from a sample containing the element M. 2 represents an electronic partition function, EMis the first ionization potential, and we shall designate Ti the ionization temperature ( 3 ) . If the Saha-Eggert equation 'Present address, Philips GmbH ForschungslaboratoriumHamburg,
2000 Hamburg 54, West Germany.
is adopted ( 4 ) ,then the proportionality constant K is given by
K = A(Ti3"/n,) exp(AE/hTi)
(2)
where A is a numerical constant, ne is the electron density, and hE is the ionization potential depression due to Coulomb interactions. Alternatively, in the Saha-Langmuir formulation,
K
(3)
= exp(c$/kTi)
where 4 is the sample work function. Finally, according to Jurela (8,
K
= exp((9
+ 6.54/a)/hTi)
(4)
where a is the largest lattice parameter. Irrespective of which K (if any) is relevant, we see that T, may be derived from a plot of log(nM+ZM/nMZw) vs. EM. For nM+,we can straightforwardly substitute I M + / q M + where Iw+ is the total measured current of M+ ions (corrected for isotopic abundance) and OM+ is an instrumental fador (viz., the fraction of nM+which is actually monitored). For nM, we can use the atomic concentration, cM,provided that nMO = nM, the latter being the total number of all M-containing species emitted per unit time. T, may then be obtained directly from the analysis sample if at least one concentration is known. The method used in this publication, however, is from measurements with a standard of similar matrix in which case many concentrations are known. Once T,has been specified, concentrations in an analysis sample can be calculated from
(5) where R denotes another sample constituent. If an overall qualitative analysis has been carried out beforehand, it is not necessary to know any one concentration since the derived concentrations can be summed to 100%. Equation 5 is a direct consequence of assuming that nM = nM, whereupon the actual magnitude of K in Equation 1 becomes unimportant. Our sole justification for the assumption is the satisfactory analytical results that ensue.
EXPERIMENTAL Samples Analyzed. The known concentrations of the sample constituents identifiable with SIMS are listed in the relevant table in the Results section. The standards NBS 93 (borosilicate glass), NBS 89 (Pb-Ba glass), NBS 128 (soda-lime glass), NBS 91 (opal glass), NBS 98 (plastic clay), NBS 97 (flint clay), and NBS 78 (burnt refractory) were supplied in powder form. Portions were pressed into pellets after admixture with spectroscopically pure graphite powder. The graphite also prevented charge buildup from ion bombardment during the analysis. NBS 610 comprises 72% SiOz,12% CaO, 14% NaPO,and 2% A1203 by weight as base material, with 61 dopants each at a nominal concentration of 500 ppm (wt). Those elemental concentrations not yet determined by NBS are given in brackets in Table I. Poor reproducibility of the initial SIMS measurements, ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
927
both laterally and in-depth, was overcome by milling the specimen into a fine powder and pellet preparation with either graphite or silver. A similar overall SIMS analysis resulted from either type of pellet, while intercomparison permitted the identification of molecular ion spectral interferences containing either C or Ag. The remainder of the standards were in massive form. The naturally-occurring mica was analyzed in our laboratory by x-ray fluorescence; those elemental concentrations determined by spectrochemical analysis are accurate only to within a factor of two or three. Microscope glass cover slips, manufactured by Chance Propper Ltd. (Smethwick, England), will be referred to as Chance glass; our x-ray fluorescence analysis agreed well with the melt composition of the manufacturer. The remaining high-purity glasses, Philips B 35 and 108, are from our laboratory; we again specify the melt compositions, plus the spectrochemical determination of potassium. SIMS Measurements. All measurements were made with a Cameca IMS 300 instrument, sometimes in an oxygen atmosphere. Usually, the samples were bombarded with a current density between 0.005 and 0.2 mA/cm2 by a 6 keV, 300-pm diameter, rastered Art beam incident at 55' to the target normal. Surface charging of the massive glasses was reduced by gold grid deposition to between +5 and +25 V, gradually increasing as the grid was sputtered away. Alternatively, when 15 keV 0- primary ions at 40' incidence were used, the charging was kept at much below -10 V by a 100-pmthick, 400-pm diameter orifice, Ta diaphragm in contact with the solid sample (6). Secondary ion currents were measured (7) in the current amplification mode as the peak height. Previously (3),we utilized automatic 500-s sweeps of the 1-260 mass range. However, we have since discovered that manual adjustment of the mass spectrometer magnet current along with optimization of the secondary ion focusing optics at each mass number of interest leads to more meaningful and reproducible measurements. Thus, one spectral run now took about 1h during which time a few pm of material could be sputtered away. Usually, only Mt currents were noted along with ZMO+ if this was comparatively large. As the mass resolution was about 300, spectral coincidences had to be taken into account by using natural isotopic abundances, e.g., 56Fet was corrected for z8Si2tcontributions, GsZntand @Gatfor any Ba2+,etc. Secondary ion currents were always referred to Isl+,which was recorded as often as was warranted by its constancy during the erosion. With the gridded specimens, all signals slowly increased because of more sample surface being exposed by the gradual removal of the grid, and hence Is,+was noted after each reading. Lateral homogeneity was tested by measuring at another spot on the sample surface. Generally, a relative secondary ion current was reproducible to better than 20%. Since readings were made usually at only 2 to 4 sample positions, rigid homogeneity test were not performed. The Pb in NBS 91 (0.009 at.%) proved much too inhomogeneously distributed for meaningful determination.
RESULTS Effect of Oxygen Admission.
With increasing O2 pressure, the '*Sit signal from Ar' bombardment increased (except for NBS 97) about 1.7 times followed by a slow decrease. Thus, measurements were made both in vacuum and in sufficient O2 to just maximize Isi+. Slight changes, but of differing magnitudes, were found in most other M+ currents ranging from intensity decreases for those elements with low ionization potentials through to intensity increases for the high EM elements. Io+ itself increased about 3 times. IMo+also increased as did the currents of those molecular ions containing hydrogen. For Ozf or 0- bombardment, only decreases in Isi+were found upon O2admission so that measurements were made in vacuum alone. Derivation of T,. T, was calculated from the least-squares slope of the straight line in a plot of log (IM+ZMO/CMVM+ZM+) vs. EM. As many points as possible were used by considering all sample constituents (major and minor elements) on an equal basis. EMwas taken from the literature (8, 9). For several standards, the influence of ?M+ and 2 on the straight line fit was examined. Noting a systematic dis928
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
I
b)
\
-2 01
0
Be
6
7
8
9
E, lev1
Figure 1. Log of reduced ion current h+ divided by atomic concentration c,vs. ionization otential &. h+ is the product of the measured current &+,(mass and the atom-to-ion partition function ratio at T, Crosses result when Lo+is added to &+
NO.)'^,
crimination against the heavier elements, we found (as used by others (10)) that substitution of gM+ 0: (MJ"', where Mi is the mass number of the measured isotope, always improved the closeness of the fit. We now consider the effect of the partition function term (3, 11) using the analysis of 27 elements in NBS 610 (Art 0,; 40-105 eV mass spectrometer bandpass) as an illustrative example: 1. With z M o / z M t = 1, T , was found to be 29 700 K with a standard deviation of 9600 K while the log term for 48% of the elements was within a factor of 2 of the value needed for an exact straight line fit. 2. A small improvement was achieved by using the ground state statistical weights; T, was 19 100 f 4200 K with 63% of the points lying to within a factor of 2 of the straight line. 3. Temperature-independent partition functions were tried, the values calculated (12) at 5000 K being arbitrarily chosen. A significant improvement resulted since 85% of the points satisfied the above criterion, and T, was 21000 f 3400 K. 4. Finally, we considered the dependence of 2 on Ti. Values were taken from Drawin and Felenbok (13),those computed for AE = 0.5 eV being arbitrarily adopted, and from de Galan et al. (12) for the remaining elements. Extrapolation to higher temperatures was carried out when necessary. Computer iteration was made until the Ti value used for 2 coincided to within 1% with that derived from the slope. We entitle our program QUASIMS. 89% of the elements were now satisfactory, and Ti = 13 800 f 1100 K. The smaller standard deviation signifies a better straight line fit although the improvement over the previous option was not too dramatic. We have used QUASIMS in all future computations. Analytical Results. Results for NBS 610 silicate glass are given in Figure 1and Table I. Many quoted concentrations
+
Table I. Comparative Analyses of NBS 610 under Different Experimental Conditions Art: Ti= Ar' t 0,: Ti = 8 8 4 0 i 290K 800Oi 270K C M (at. %)
Li Be B Na Mg Al Si K
Ca sc Ti
0.81
24.7 0.024 4.4 [0.023] 0.019
V Cr Mn co Ga Rb
[0.020] [0.020] [0.018] 0.014 [0.015]
Sr Y
0.012 [0.012]
Zr Nb In Sn Sb cs Ba
[0.011] [0.011] [0.0090] [0.0087] [0.0085] [0.0076] [0.0075]
La
[0.0074]
Ce
Pr Nd
Sm Eu
Tb Ho
Tm
TI Pb Bi Th
a
E0.151 [0.11] 0.067 9.3 [0.042]
0.010
[0.0074] [0.0073] [ 0.00721
[0.0069] [0.0068] [0.0065] [0.0063] [ 0.0061 ]
0.00062 0.0042 [0.0049] 0.0041
I M +(a.u.)
0.16 0.0049 0.0014 16 0.013 0.31 1.0
0.17 5.5 (0.018) 0.0080 0.010
...
... (0.0042) ...
(0.0071) 0.055 0.020 (0.0044) (0.0067) (0.0023) 0.0010
0.0027 0.0011
(0.00017) 0.040
Calcd C M 0.061 0.13 0.093 8.5 0.050 1.1
25.7 0.041 3.9 (0.022)
-
(0.0001)
0.084 0.0044 0.0013 7.6 0.012
Calcd C M 0.058 0.10 0.087 8.1
0.054 0.92 27.0 0.033 3.3
0.18 1.0
0.068 3 .O
..
*..
0.0031
0.022
... *.. (0.027) ...
(0.038) 0.016 0.014 (0.013) (0.0086) 0.0052 0.012
0.0052 (0.0077 ) (0.0040) (0.0032)
*..
(0.0011)
(0.0055) 0.0026
(0.013)
(0.00018)
0.0068 0.0087 0.0070 0.0061
...
(0.023) 0.013
0.018
0.011
0.015 (0.029) (0.022) (0.024)
(0.0032) 0.022 0.0091 (0.0020) (0.0038) 0.00041 0.0017 0.00078
0.011
0.013 0.0044 0.0094 0.0039 0.0092 0.0046 0.0085 0.0048 -0.0091 0.0061 -0.0091 0.0096 0.012 0.0023 0.0046 0.0023 -0.0035 0.0016 0.0023 (0.00016) 0.00021
I M +(a.u.)
0.017 0.0045 0.0056 0.0014 0.0038 0.0012 0.0037 0.0014 0.0034
0.011
-0.0091 0.013 -0.0065 -0.0063 0.0053 (O.OOl0)
0.0033 (0.0036)
0.00026 0.00070 0.0009 U 0.0040 0.00025 0.0011 0.00068 40-105 eV secondary ion energy bandpass utilized.
are only nominal (denoted by brackets in the table), and the assignment of mass peaks is complicated by the large number of molecular ions. The usefulness of high mass resolution in unravelling this spectrum has already been demonstrated (14). Comparison with the spectrum of NBS 612, which contains 50 ppm (wt) of the same dopants, enabled us to positively identify some atomic ion signals. Figure l a shows that elements with appreciable MO' currents appear to have too small reduced atomic ion currents. (Zr and Nb are amongst these elements (3, 7) but their monoxide ion currents could not be reasonably estimated.) For a given element, the deviation from the straight line increased with increased MO' formation, Le., from working in an oxygen atmosphere. Fairly satisfactory results (except for T h and U) were obtained by simply adding IMO+to IMt
I,+
(a.u.)
0.0064 0.0032 0.0012 0.67 0.0036 0.070 1.0
0.0029 0.95 (0.0036) 0.0019
Calcd C M 0.037 0.052 0.061 8.3 0.032 0.83 26.1 0.017 4.3 (0,019) 0.014
(0.0017) (0.0013) (0.0012) (0.00038) (0.00044) 0.00083 0.0019 (0.0016)
(0.011) (0.012)
(0.0012) 0.00055 0.00021 -0.00018
(0.016) 0.0056 0.0038 -0.0040
0.00052 0.0013
0.0046 0.0079
0.00091
0.0051
0.00092
0.0046
0.00095
0.0046
0.00095
0.0048
0.0011
0.0066
0.00093
0.0058
0.00058
0.0043
0.00054
0.0047
-0.00045
-0.0045
... ... ...
... ... ...
(0.011)
(0,0089) (0.0053) 0.0058 0.010
(0.013)
(0.010)
0.011
0.015 (0.013) 0.011
...
...
0.0054 0.0055 0.0045 0.0038
0.0013
-0.0071
Ar' t 0,: T i = 1 3 730 i 889 Ka
-0.0035 0.0017 -0.0029 0.0019 0.0027 0.00091 -0.0021 0.00091 -0.0016 0.00065 0.0010
(0.000076) 0.00018
(0.000069) 0.00015
-0.0044 -0.0045 0.0045 -0.0045
- 0.0044 0.0035 (0.0006) 0.0035 (0.0028)
0.00051
0.0008
0.00014 0.00048
0.0009
0.00013 -0.00026 0.00013 -0.00026
-0.0009
- 0.0011
(3, 11))or by monitoring only higher-energy secondary ions (Figure 1b) whereupon the IMo+to I,+ ratios were substantially reduced. This latter procedure decreased Isi+only 9 times but some other M+ currents much more. Note the higher T, value now pertinent. Parentheses in Table I indicate an upper limit determination since no isotope check was possible. An approximate reading signifies (a) some irreproducibility, (b) a rather weak, fluctuating signal, or (c) that a fairly substantial, molecular ion correction was made. The larger ion current given for some elements refers to (IMO+ + IM+)which was used for the dewas obtained from the other standards, and termination. ITi0+ I H d + from plots such as Figure 2. The partition function ratio of La was used for the lanthanides, while the set values for T h and U were derived at 5100 K (15). For improved results, ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
929
Table 11. Comparative Analyses (at. %) of Glasses and Ti Values NBS 89 8860 + 240 K
Art :
NBS 9 1 8840 i: 300 K
Calcd
CM
Calcd
B
...
...
...
...
0
61.4 4.6 0.018 0.088 27.0 0.08 4.4 0.093
72.2 3.4 0.016 0.086 18.7 -0.042 4.2 0.085
57.3 5.6
59.8 5.6
CM
Na Mg A1 Si P
K Ca Ti Fe Sb Ba Pb Art
... ...
*.. ...
...
+
...
0.23 1.9 0 , : 9750
*
-
0,':
-
...
2.4 23.1
2.7 21.7
1.4 3.8
1.8 2.0
...
...
... *.. ... ...
*.. ...
...
0.20 0.89 430 K
0-:
...
*..
...
...
9270
f
NBS 93 8910 i 210 K Calcd
CM
Chance 9190
Calcd
CM
i
310 K
Calcd
CM
7.0 64.1 2.55 0.012 0.72 25.5
10.2 59.0 2.2 0.011 0.96 27.5
0.89 59.5 11.1 1.7 0.76 23.7
0.77 67.7 10.1 1.4 0.82 17.1
3.2 59.8 8.2 0.50 1.5 22.3
5.9 61.2 5.8 0.60 1.7 20.2
0.065
0.058
0.43 1.7
0.59 1.3
1.6 0.83 0.56
1.9 0.63 0.67
.,.
0.0064 0.018
9800
... ...
...
... ...
0.065
...
e
* 430 K
.
.
9220
10600 f 780 K 9390 ?: 340 K
...
*..
., . ...
'(0:0084) 0.024
... ...
...
...
...
*..
1180 K
-
NBS 128 8760 i 190 K
...
...
0.057
... * 430 K
0.093 0.19
...
...
...
0.046 0.16
...
9940 f 480 K 9820 t 490 K -
-
-
Table 111. Comparative Analyses (at. %) of Mica, Silicates, and Glasses Mica NBS 98 NBS 97 NBS 78 B 35 Glass 108 Glass Art : 8910 ?: 350 K 8890 f 360 K 8670 ?: 320 K 9270 i: 120 K ... CM Calcd CM Calcd CM Calcd CM Calcd CM Calcd CM Calcd Li -0.014 0.0038 0;045 0.0092 0.36 0.13 0.28 0.12 ... ... ... ... ... ... ... ... ... B -0.019 0.016 *.. ... ... ... ... ... 68.3 63.2 66.3 60.9 60.2 0 63.7 67.3 58.8 61.5 58.6 ... 0.24 0.065 0.040 0.055 Na 0.90 0.19 0.053 9.6 0.62 5.4 5 .O 13.6 0.26 0.083 0.26 0.24 ... ... ... 0.37 0.40 0.15 0.33 ... Mg
AI
Si P K Ca Ti Fe As
14.7 16.0
... 7.0 *..
0.054 0.73
...
13.9 17.5
... 6.8 ...
0.074 -0.41
...
Ba -0.007 0.004 Art + 0,:I 0-: 9560 ? 730 K
11.2 21.9
...
1.5 0.083 0.40 0.55
...
11.8 17.3
...
1.6 0.054 0.16 -0.35
...
0.0087 0.0091 9000 i: 600 K
18.0 16.8
...
...
0.27 0.042 0.70 0.27
0.30 -0.013 0.34 -0.35
*..
*..
-0.0023
_.
the values calculated (13)with AE = 0.1 eV were used for Li and Na. Tables I1 and I11 contain the results for the other standards. Oxide corrections were made for Ti and Ba. Note that 6 keV Ar' bombardment led to a satisfactory determination of oxygen. Bombardment in oxygen again increased Ti to a value similar to that found with 6 keV 02' or 15 keV 0- bombardment in vacuum. For mica, the surface charging was deliberately increased (6) to -50 V, thereby increasing Ti to 11660 f 1120 K. Negative charging erects a surface potential barrier which discriminates against the emission of lowerenergy positive ions. With the 40-105 eV bandpass and 0projectiles, T , values of 13 040 f 2470 K and 13 520 f 1160 K were measured for mica and Chance glass, respectively. We see from Table I11 that T , and the analytical accuracy remain essentially unchanged when Al is the main cationic component. IF+ from NBS 91 was about lo3 times larger than expected and therefore F (6.2 at. 70)was omitted from the analysis; others also mentioned (16, 17) difficulties with this element.
DISCUSSION Analytical Accuracy. The first essential for analytical accuracy is for as accurate a specification of Ti as possible. For glasses and silicates, it appears that a value of 8900 K should be adopted for an initial estimation of the makeup of an unknown sample when Ar' bombardment in vacuum is used. A value of 9500 K is preferable if the analysis is 930
16.3 16.0
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
0.0013
-
24.2 5.7 -0.077 1.5 0.071 0.63 -0.097
28.6 7.2 0.18 1.3 0.14 0.88 0.19
...
...
...
9350
...
f
780 K
_I
...
23.8
...
8.2 3.4
...
... ... 20.8 23.7 ... ...
28.8
...
0.014 2.6
9.1 -0.009 3.1 3.4
... . * * *.. ... * . . ... ... 0.68 . . . . . . . . .
...
...
9560 9800
* *
300 K 350 K
-
... 0.42 ...
9210 i 720 K
performed in an oxygen pressure sufficient to maximize Isit, or if 02+ or 0- primary ions are utilized. The chosen primary ion energy does not appear to play an important role. These values should be increased to about 11000 and 13000 K, respectively, if measurements are confined to secondary ions with energies 140 eV. A more precise determination of T ,can then be accomplished from measurements with a standard of similar matrix if available; the standard should contain as many specified elements as possible over a wide range of first ionization potentials. This T , value could then be used for a better estimate of the remaining elements present in the sample but not in the standard. On the other hand, if one concentration is known beforehand, various sample compositions can be derived from Equation 5 by using arbitrary T,values and that adopted in which the calculated concentration of the given element most closely matches its real value. This approach was tested on NBS 93 using each element in turn as the internal standard. Scarcely no loss in analytical accuracy resulted since T,values in the range 8920 to 9040 K were found. For further discussion, we shall assume that Ti is known. as the experimental value We define an error factor, &+/cM), of i M + / c M divided by that required for an exact fit to the straight line in a plot of log(iM+/CM)vs. &. Normalization of the calculated concentrations to 100% (or to about 40% if oxygen is excluded) always weights the analysis in favor of as an inthe major elements. Therefore, we use E(~M+/cM)
dicator of the analytical precision that can be expected for a given element irrespective of the sample matrix. We found that €(iM+/CM) for nearly d l constituents turned out to be less than a factor of two. Remember, however, that this accuracy may not be necessarily attained in an actual trace element determination unless the c(~M+/cM) value of the matrix element is close to unity. Also, in the one internal standard approach, the accuracy will depend upon the error factor of the element whose concentration is known. In the Ti range of 8-10000 K, consistent c ( ~ M + / c M ) values of 0.35 (Li), 1.25 (B), 1.2 (O), 02 1.15 (Al), 1.3 (K), 0.71 (Ca), and 0.83 (Ba, when using Ina+ VP,y l e v i IBao+) were indicated from the present standards. It may prove Flgure 2. Secondary ion current ratio of MO’ to M+ as a function of advantageous in future analyses to divide iM+ by these the dissociation energy of the neubal monoxide molecule V ,O for various quantities. rare earths in NBS 610 (Ar’ 02; 0-105 eV bandpass) For those elements with appreciable MO’ currents, cor) IMO+/IM+ rections can be made (3, 7,171 from ~ ( ~ M + / c Mvs. 21 700 f 2700 K. (The standard deviation has been derived plots. Since this latter ratio is not too large for these insulator is known precisely.) The value by falsely assuming that VMOO standards, use of ( I M + + IMo+)should also prove fairly satof Td is perhaps not too significant since in its derivation both isfactory. Another alternative involves monitoring of highthe partition function and ionization potential terms in er-energy secondary ions only, with the inherent danger, Equation 6 have been neglected. however, that the number of sputtered atoms in the energy range chosen is no longer representative of the sample CONCLUSIONS composition. It appears that survey analyses with SIMS should be We finally consider some origins of nonrandom errors in feasible with a single-parameter method. Future developments the experimental (iM+!cM): require determining T,values for standards of different 1. The approximation nMO = n M . For low EM elements, matrices, in the hope of obtaining a reasonable estimate of E(iM+/CM+) might appear to be below unity because of an this parameter for a sample in which no concentrations are appreciable n M + , and would decrease even further as Ti inknown. By simultaneously cataloguing error factors for each creased. For those elements forming strong bonds with element at various Ti values, it should prove possible to oxygen, n M O o and/or nMO+ might be significant again leading improve the analytical accuracy obtainable. to an apparently low €(iM+/CM); higher sample oxygen content ACKNOWLEDGMENT would then increase the discrepancy. However, we attribute (7) the divergence of those elements with substantial MO’ The invaluable assistance of H. M. Wielink in sample currents primarily to their tendency to emit these ions rather preparation, data acquisition, and computation is gratefully than low energy M’ ions, Le., the error results mainly from acknowledged. Many thanks are also due to P. D. M. Keehnen IM+being too low compared to other elements. and J. v.d. Berg for developing the computer program. 2. The apparatus constant encompasses the efficiency of LITERATURE CITED (a) ion collection into the mass spectrometer, (b) transmission V. Leroy, J.P. Servais, and L. Habraken, Metall. Rep. CRM, 35, 69 (1973). through this spectrometer, and (c) photomultiplier detection. T. Ishizuka, Anal. Chem., 46, 1487 (1974). Clearly, the simple correction factor (MJ1’’could be improved A. E. Morgan and H. W. Werner, Anal. Chem., 48, 699 (1976). C. A. Andersen and J. R. Hinthorne, Anal. Chem., 45, 1421 (1973). upon. 2 . Jurela, Int. J. Mass Spectrom. Ion Phys., 12, 33 (1973). 3. Partition function ratio uncertainties, particularly for H. W. Werner and A. E. Morgan, J. Appl. Phys., 47, 1232 (1976). larger T, values. One might also query if the relevant temA. E. Morgan and H. W. Werner, Surf. Sci. (in press). Ch. E. Moore, NSRDSNBS 34, “Ionization Potentials and Ionization Limits perature is necessarily equivalent to Ti. Derived from the Analyses of Optical Spectra” (1970). Monoxide Ion Formation. Assuming an expression W. C. Martin, L. Hagan, J. Reader, and J. Sugar, J. Phys. Chem. Ref. Data, 3, 771 (1974). analogous to Equation 1, we may write that
+
+
where VMoo and EMOare, respectively, the bond dissociation energy and the ionization potential of the neutral monoxide molecule, and Td is the dissociation temperature. In agreement with Ishizuka (2), Figure 2 shows that a plot of log (IMo+/IM+) vs. VMOO(taken from Ref. 18) is linear for the rare earths. This suggests that for these elements, the partition function ratios are comparable as is the difference between EMand EMO.As found also for Ar’ bombardment in vacuum, the IMO+/IM+ ratio increases with increasing VMOO, and Td =
R . Shimizu, T. Ishltani, and Y. Ueshirna, Jpn. J. Appl. Phys., 13, 249 11974). b. S. Simons, J. E. Baker, and C. A. Evans, Anal. Chem. 48, 1341 (1976). L. de Galan, R. Smith, and J. D. Winefordner, Spectrochim. Acta, Part 6 ,23, 521 (1968). H. W. Drawin and P. Felenbok, “Data foc Plasmas in Local Thermcdynarnic Equilibrium”, Gauthier-Villars, Paris, 1965. D. K. Bakale, B. N. Colby, and C. A. Evans, Anal. Cbem., 47, 1532 (1975). C. H. Corliss, J. Astrophys., 136, 916 (1962). J. R . Hinthorne and C. A. Andersen, Am. Mineral., 60, 143 (1975). C. A. Andersen, Natl. Bur. Stand. ( U . S . ) Spec. Pub/.. 427, 79 (1975). 6. Rosen, “SpecWoscopic Data Relawe to Diatomic Molecules”, Pergamon Press, New York, 1970.
RECEIVED for review November 11, 1976. Accepted March 15, 1977.
ANALYTICAL CHEMISTRY, VOL. 49. NO. 7, JUNE 1977
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