The electronic partition functions of atoms and ions between 7000 and 12000 K

Specrrochmica Acm. Vol. 429, No. Printed m Great Bntain

IO, pp

1105-l

0584-8547/87

I1 I, 1987 0

1987 Pqamon

E3.00 + 0.00 Journals

Ltd.

The electronic partition functions of atoms and ions between 7000 and 12 000 K SHOZO TAMAKI*

and TSUKASA KURODA~

Osaka Prefectural Industrial Research Institute, 2-1-53 Enokojima, Nishi-ku, Osaka 550, Japan (Received 3 February 1987; in revised form 19 May 1987) Abstract-The electronic partition functions of atoms and singly-charged positive ions are presented, for 52 elements, in the form of the second-order polynomials of temperature, which are valid between 7000 and 12 000 K. The errors in the partition functions calculated with these polynomials are, at most, of the order of 1% for most of the elements listed. The limitations of the results and the causes of errors are discussed.

1. INTRODUCTION THE ELECTRONICpartition function is an important factor for the interpretation of experimental results in atomic [l, 23 and molecular spectroscopy [3,4]. It also plays a great role in the concentration calculation using the Saha-Eggert equation in secondary-ion mass spectrometry (SIMS) [S, 63. Numerical values of the partition functions at specified temperatures have been presented for many elements [l, 7-93. It was suggested that their temperature dependence [lo] should be seriously taken into consideration. For temperatures between 2000 and 7000 K, BOUMANS [ 11,123 has suggested the use of temperature dependent “corrections” of excitation potentials in the Boltzmann equation and of ionization potentials in the Saha-Eggert equation to account for the partition functions. Numerical values of such corrections were given for temperature intervals of 1000 and 6000 K for excitation and ionization potentials, respectively. CAPITELLOand FERRARO[ 133considered cut-off criteria of electronic partition functions calculated according to four different theories. It is often necessary, however,to calculate the values of the partition functions at arbitrary temperatures. These data are not readily available in the literature. DE GALAN et al. [lo] have presented the partition functions for atoms and singly-charged ions of 73 elements in the form of the fifth-order polynomials of temperature. These expressions are valid for the temperature range between 1500 and 7000 K. They have been subsequently used, for example, in the quantification of SIMS [14, 151. As the temperature rises above 7000 K, however, substantial discrepancies occur between the values presented by DRAWIN and FELENBOK [9] and those calculated with the polynomials of DE GALAN et al. It has been impossible to obtain the partition function accurately at arbitrary temperatures higher than 7000 K. The present paper gives the electronic partition functions of atoms and singly-charged ions for 52 elements as the second-order polynomials of temperature, viz.

Z(T) = A(z-/103)2 + B(T/103)+C.

(1) The values of the coefficients are valid for temperatures between 7000 and 12 000 K. With the aid of the polynomials of DE GALAN et al. [lo] and those of the present authors, one can obtain the numerical values of partition functions at arbitrary temperatures between 1500 and 12000K. 2. METHODS The present research determined the polynomial coefficients A, B and C in Eqn (1) by a least squares fit to the data shown in Table 1. The data for 39 elements were the numerical values presented by

*Author to whom correspondence should he sent. +Present address: Institute of Scientific and Industrial Research, Osaka University, 8-l Mihogaoka, Iharaki 567, Japan. 1105

SHOZOTAMAKIand TSUKASAKURODA

1106

Table 1. Data used for the determination of A, E and C in Eqn (1). The 13 elements are those for which the values of partition functions are not presented by DRAWINand FELENBOK[9] Data used for least squares fit 39 elements

Atom Ion

13 elements (labelled + in Table 2)

Atom Ion

Partition functions between about 7000 and about 12000 K presented by DRAWINand FELENBOK[9] Partition functions between 3750 and about 12000 K presented by DRAWINand FELENBOK[9] Partition functions calculated with the polynomials of DE GALAN et al. [lo] for 500 K intervals between 5000 and 9000 K

Table 2. Values of A,B and C in Bqn (1) for atom (I) and singly-charged ion (II). The column “No. of data” lists the numbers of numerical values of partition functions between To and F, used for the least squares fit. For the elements labelled 7, Eqn (1) was fitted to the partition functions calculated by the polynomials of DE GALAN et al. [lo] Element

4s 1

Ag II Al I Al II Ar I Ar II As I+ As II+ Au I+ Au II+ BaI Ba II Br I Br II CI c II CaI Ca II Cd I Cd II Cl I Cl II co I co II Cr I Cr II cs I*. cs II’ cu I cu II FI F II Fe I Fe II Ga I’ GaII+ HI H II He I He II Hg I

A 7.7292 E-2 5.1919 E -3 1.4928 E-l 2.9986 E-3

B -1.1810 -6.9130 -2.0223 -3.5789

E 0 E-2

E 0 E-2

O.OOOoE 0

O.OCKIOE 0

-2.1925 E-3 2.5553 E-2 -4.1618 E-2 -4.0428 E-3 3.7825 E-2 4.7490 E- 1 -2.6956 E-3 2.2647 E-3 - 1.2363 E-2 1.1205 E-2 3.0579 E-3 3.4326 E- 1 1.2888 E-2 3.4178 E-2 1.2331 E-3 2.5888 E-3 - 5.2246 E - 3 1.1086 E 0 - 7.0808 E - 2 1.1741 E 0 2.9217 E- 1 4.3178 E- 1

8.0383 E-2 6.7896 E - 2 1.0640E 0 3.1342 E- 1 -2.8191 E- 1 -4.8168 E 0 5.7097 E-l 4.7192 E-2 5.2832 E- 1 2.2139 E-2 -3.8311 E-2 -4.6083 E 0 9.2116 E-2 - 5.2518 E - 1 - 1.5376 E-2 -1.1225 E-2 3.0834 E - 1 -1.2125 E+l 4.4949 E 0 - 1.3021 E + 1 -2.0561 E 0 -3.8388 E 0

O.OOOOE 0

O.OOOOE 0

5.4196 E-2 1.8540 E-2 -2.1451 E-3 -5.7894 E-5 1.7361 E 0 1.7050 E- 1 -5.9079 E-2 O.OoOOE 0 3.3336 E-4 undefinable

-4.9475 E-l -1.4679 E-l 5.5623 E-2 1.0189 E- 1 -2.1190 E+l 2.2556 E 0 8.4502 E - 1

O.OOOOE 0 O.OOOOE 0 7.6274 E - 3

O.OOOOE 0 O.OOOOE 0 - 1.1717 E- 1

O.OOOOE 0 -5.6487

E-3

c

No.of data

To (K)

& (K)

6.5616 E 0 1.2198 E 0 1.2906 E+ 1 1.1005 E 0 l.OOWE 0 5.0313 E 0 3.4981 E 0 1.6134 E 0 9.6792 E - 1 1.5969 E 0 1.6006 E+l 1.5562 E 0 4.5002 E 0 4.4042 E 0 8.8798 E 0 6.0588 E 0 1.7404 E+ 1 1.3582 E 0 3.0361 E 0 2.0428 E 0 5.6257 E 0 6.9708 E 0

13 5 9 8 12 4 9 9 9 9 9 13 13 5 14 5 13 13 13 11 13 4 13 10 9 11 5

6929 5250 6964 4500 3750 6750 5000 5ooo 5000 5000

12444 12 155 10290 12060 12216 14883 9000 9000 9000 9000 10 290 12033 12005 12 155 12606 13891 12348 12005 12 286 12410 12 256 12678 12444 12 558 10 159 12410 6174

13 6 10 4 13 11 9

6929 5000 4250 8500 6929 4000 5000

12444 12 155 12 558 18 742 12444 12410 9000

13

6824

12256

13

6700

12033

7.3941 E+l 8.7206 E 0 4.9842 E + 1 9.9904 E 0 1.0871 E+l l.OOOOE 0 3.7239 E 0 1.2942 E 0 5.5470 E 0 8.0353 E 0 1.0037 E+2 2.7436 E + 1 2.3711 E 0 l.OOOOE 0 2.0235 E 0 l.OOOOE 0 2.OOOOE 0 1.4505 E 0

6700 6685 5250 6685 6000 6876 6685 6841 4000 6824 5750 6929 4250 6876 4Otm

Electronic partition functions

1107

Table 2 (continued) Element Hg II II I I1 In I In II Ir I+ Ir II+ K I* K II* KrI Kr II Li I Li II MgI Mg II Mn I+ Mn II+ MO I MO II NI N II Na I Na II Nb I+ Nb II+ Ne I Ne II Ni I Ni II 01 0 II P I+ P II+ Pb I Pb II Pt I+ Pt II+ Rb I* Rb II* Re I+ Re II+ SI s II Si I Si II Sn I+ Sn IIt Sr I Sr II Ta I+ Ta II+ Ti I Ti II v I+ v II+ w I+ w II+ Xe I Xe II Zn I Zn II Zr I Zr II

A 2.9681 9.7102 -3.9048 2.0733 1.5042 - 7.4275

E- 3 E-3 E-3 E- 1 E- 3 E- 2

7.2641 E-l 0.OOOOE 0 6.5237 E-4 -4.0070 E-3 2.5279 E - 1 0.OOOOE 0 1.0932 E- 1 2.2113 E-3 7.8764 E - 1 4.6990 E - 2 8.6252 E- 1 3.5556 E - 1 1.2776 E-2 5.0004 E-4 2.9025 E- 1 0.OOOOE 0 9.2795 E - 1 - 1.2334 E- 1 0.OOOOE 0 -4A499 E-4 6.1106 E- 1 2.0558 E-2 2.9215 E-3 4.5272 E-3 3.5558 E-2 -9.1980 E-2 1.8072 E- 1 4.3310 E-3 1.7621 E-l 8.8186 E-2 1.1609 E 0 (20000E 0 3.1349 E- 1 2.2798 E- 1 1.1417 E-2 7.6889 E- 3 2.2473 E - 1 -8.7074 E-4 -4.3208 E-2 2.4764 E-2 2.7823 E- 1 1.9160 E-2 6.0013 E- 1 1.7954 E- 1 9.0184 E- 1 4.6027 E-2 4.8996 E- 1 7.1496 E-2 1.4626 E- 1 3.1895 E- 1 7.5260 E-3 -8.6366 E-4 2.3875 E-2 1.5341 E-3 2.5937 E 0 2.2446 E-4

B -3.5464 -6.9130 3.6218 -2.6861 -1.8883 4.9438

E-2 E-2 E- 1 E 0 E-2 E 0

-8.3969 E 0 O.OwOE 0 - 1.0990 E-2 1.5500 E- 1 -3.5744 E 0 0.OOOOE 0 - 1.6363 E 0 -2.4424 E-2 -6.9643 E 0 1.5612 E- 1 -7.7998 E 0 -1.5131 E 0 -4.4140 E-2 1.2966 E- 1 -3.7354 E 0 0.OOOOE 0 5.9668 E- 1 1.1085 E+ 1 O.OcwE 0 2.2598 E-2 -7.6721 E 0 1.3931 E 0 7.2856 E-2 1.7232 E-2 -7.6124 E-2 1.4547 E 0 -2.4407 E 0 2.1753 E-2 -8.9169 E-I 4.7131 E-l -1.5231 E+l O.OODOE 0 -1.6690 E 0 -1.6779 E 0 5.8682 E - 2 1.4278 E - 1 -3.2624 E 0 5.5897 E - 2 1.1828 E 0 -6.3973 E-2 -3.3006 E 0 -2.2881 E-2 -1.1255 E 0 4.0460 E 0 -3.2389 E 0 4.1960 .E 0 3.1278 E 0 5.8599 E 0 2.5768 E 0 1.3458 E- 1 - 1.2727 E - 1 8.2439 E-2 -3.7121 E-l -2.5760 E-2 - 2.6630 E + 1 7.2385 E 0

C 2.0997 4.4328 3.9132 1.3381 1.0547 -1.7283

E 0 E 0 E 0 A%+I E 0 E 0

2.7351 E+ 1 l.OOOOE 0 1.0455 E 0 3.7664 E 0 1.5171 E+ 1 l.OOOOE 0 7.2783 E 0 2.0617 E 0 2.2945 E+ 1 5.7373 E 0 2.7393 E+ 1 5.4235 E 0 3.8867 E 0 8.1160 E 0 1.4477 E+ 1 l.OOOOE 0 2.6792 E-t 1 -9.6165 E 0 l.OOOOE 0 5.604OE 0 5.8508 E-t 1 3.4072 E 0 8.3973 E 0 3.6317 E 0 3.8940 E 0 3.5860 E 0 1.0604 E+l 1.8719 E 0 1.9971 E+ 1 5.1914 E 0 5.3941 E+l 1.OOOOE 0 8.0420 E 0 1.0311 E+l 8.4502 E 0 3.1808 E 0 2.2124 E+ 1 5.4015 E 0 3.0386 E- 1 2.9060 E 0 1.1651 E+l 1.7712 E 0 7.6848 E 0 -2.2029 E 0 2.3138 E+ 1 3.2435 E + 1 1.9368 E+ 1 1.2089 E+ 1 -3.9664 E 0 2.1689 E 0 1.5309 E 0 3.7019 E 0 2.46OOE 0 2.1105 E 0 1.1523 E+2 1.1910 E+ 1

No. of data

To (K)

C (K)

8 13 7 9 8 9

4500 6700 4750 6964 4500 wxi

12060 12033 12 124 10290 12060 9000

5

6450

8232

13 5 9

6824 6000 6964

12256 13891 10290

13 12 9 9 9 10 13 4 9

6929 3750 5ow 5000 6929 8000 7w 7250 6964

12444 12216 9000 9000 10238 12410 12570 15986 10290

9 9

5000 5ooo

9000 9000

4 13 8 13 4 9 9 13 12 9 9 5

10250 6929 4500 6824 8750 5Ow 5Otw 6929 3750 5000 5000 6772

9 9 13 4 13 11 9 9 9 13 9 9 13 13 9 9 9 9 13 5 13 9 13 13

5000 5000 6700 57% 6841 4Ow 5Ooa 5000 6964 6685 5000 5ooo 6876 6824 5000 5000 5Ow 5000 6945 5250 6980 8500 6876 7ooo

22 601 12444 12060 12256 19 293 9000 9000 12444 12216 9000 9000 8232 9000 9wO 12033 12678 12286 12410 9OCm 9000 10290 12005 9000 9000 12348 12256 9000 9000 9000 9Ocm 12473 12 155 12 536 12558 12 348 12 570

1108

SHOZOTAMAKIand TSUKASAKURODA

DMWIN and FELENB~K[9], taken as the basis of the present study. The values vary with AE, the depression of ionization energy due to the Coulomb interaction of charged particles in the plasma. The values for AE = 0.10 eV [9] were used. For the singly-charged ions of these elements, the values are given between 7000 and 12@00K [9] with relatively large temperature intervals, so that a value for a temperature below 7000 K was added to make the fit more accurate. For 13 other elements (labelled t in Table 2) for which the partition functions are not given by DRAWIN and FELENBOK [9], Eqn (1) was fitted to the values calculated with the polynomials of DEGALAN et al. between 5000 and 9000 K using 500 K intervals. The present paper uses three kinds of partition functions, abbreviated as follows: Z(DF): those presented by DRAWINand FELENB~K[9]. Z@--j): those calculated with the polynomials of DE GALAN et al. [lo], Z(ABC): those calculated with Eqn (1) and the coefficients A, B and C in Table 2.

3. RESULTS AND DISCUSSION Table 2 shows the values of A, B and C in Eqn (1) for 52 elements. If we take Ag as an example, for Ag I, 13 values of partition functions were available between 6929 and 12 444 K, and for Ag II, four values between 10 500 and 12 155 K and one at 5250 K, as shown in Table 3. Table 3. Values of partition functions Z(DF) for Ag I and Ag II used for the calculation of A, B and C in Table 2 Ag II

Ag I No. 1 2 3 4 5 6 7 8 9 10 11 12 13

T(K) 6929 (= To) 7276 7640 8022 8423 8844 9286 9750 10238 10750 11287 11852 12444 (= T,)

Z(DF)

No.

2.033 2.047 2.068 2.097 2.139 2.197 2.277 2.389 2.543 2.752 3.033 3.407

1 2 3 4 5

T(K) 5250 (= To) 10500 11024 11576 12 155 (= T,)

2

3

1.000 1.067 1.088 1.115 1.147

3.897

Cr-ATOM(I).

0-l

Z(DF)

4

5

6

7

TEMPERATURE

ION

8

9

(x 1000

IO

II

12

K)

Fig. 1. Temperature dependence of partition functions, Z (a-f) and Z (ABC), for Cr I and Cr II. Solid circles show the values Z (DF) presented by DRAWINand FELENBOK[9].

1109

Electronic partition functions

The last three columns in Table 2 show the numbers of these values and the temperatures used for the least squares fit for each element. Figure 1 demonstrates the temperature dependence of two types of polynomials Z (a-f) and Z (ABC) both for Cr I and Cr II. The numerical values Z (DF) by DRAWINand FELENBOK [9] are presented by solid circles in the figure. It is clear that they are right on the curve of Z (u-f) below 6000 K, and on that of Z (ABC) above 7000 K. This situation was also seen for other elements. These facts indicate how accurately the partition functions can be obtained between 1500 and 12000 K with the aid of the two types of polynomials. 3.1. Remarks on K, Rb and Cs The three elements, K, Rb and Cs, labelled * in Table 2, entail two problems. First, only a few values of partition functions between 7000 and 12 000 K are presented by DRAWINand FELENBOK [9]. The numbers of partition functions available for these elements are: 0 for Cs I, Cs II and Rb II, four between 7111 and 8232 K for K I and Rb I, and one at 7750 K for K II. For this reason the partition functions for below 7000 K were also used in the calculation, as shown in Table 2. Yet the data are still insufficient. Second, there are no data available at temperatures higher than 8232 K. The atoms of K, Rb and Cs have low ionization energies and they are ionized at relatively low temperatures, indicating that the partition functions at very high temperatures may not be of practical importance. The singly-charged positive ions of these elements have large ionization energies because of the closed shells. Though their partition functions between 7000 and 12 000 K are not given by DRAWINand FELENBOK,it is evident that the values should be 1 [9]. This is also the case for Na. It is natural to consider that the errors in the partition functions due to this lack of data increase with temperature. Table 4 shows the comparison of Z (DF) and Z (ABC) for the atoms of K and Rb. The former are available only below 8232 K, and in calculating the partition functions for higher temperatures using A, Band C for the alkali atoms, it should be taken into consideration that the errors are larger than a few %, at least. 3.2. Errors introduced by data extrapolation The published data of the electronic partition functions are the basis of the present procedure. The use of the least squares method is justified when many data are available in the relevant temperature range. Moreover, it may be necessary to use the data for other temperatures as well. The errors introduced into the partition functions by such an extrapolation are tested here for Fe I. The values of A, B and C for Fe I in Table 2 were obtained using the 13 values of the partition functions between 6929 and 12 444 K. When only the seven values between 5079 and 6945 K would be used, the results would be A = 4.0181 E - 1, B = - 5.6338 E - 1 and C = 2.0550 E + 1. The values of the partition functions calculated with these two sets of coefficients are compared in Table 5 for three temperatures. The errors are very small in case (a) (13 data without extrapolation), while those in case (b) are large and rapidly increase with temperature. This was also found for other elements. It can be concluded that generally errors larger than a few % in the partition functions will result if an extrapolation is made over 1000 K. 3.3. Remarks on the 13 elements labelled 7 in Table 2 The data for the least squares fit were obtained with the polynomials of de Galan et al. for the 13 elements for which the partition functions are not given by DRAWINand FELENBOK [9]. Table 4. Comparison of Z(ABC) with

KI Rb I

Z(DF) for

K I and Rb I

T(K)

Z(DF)

Z( ABC)

Rel. error (%)

7111 8232 7111 8232

4.416 7.411 4.402 7.076

4.372 7.453 4.334 7.227

- 0.996 0.567 - 1.55 2.13

1110

SHOZO

TAMAKI

and

TSUKASA

KURODA

Table 5. Comparison of Z (ABC) for Fe I obtained (a) with 13 values between 6929 and 12444 K, and (b) with seven values between 5079 and 6945 K from DRAWIN and FELENBOK

[9]

@I

64

8022 9750 11852

Z(DF)

Z (ABC)

Rel. error (%)

Z (ABC)

42.758 58.939 92.937

42.099 58.793 93.087

- 1.5 - 0.24 0.16

41.888 53.254 70.315

Rel. error (%) -2.0 -9.7 -24

Since the polynomials are valid between 1500 and 7000 K [IO, 161, great care should be exercised when using them at temperatures higher than 7000 K. This is illustrated in Fig. 2 for elements for which Drawin and Felenbok list partition functions. The figure shows the temperature dependence of the two types of partition functions for Cu I and Ni I. An analogous dependence was obtained for Cu II and Ni II. Figure 2 and similar plots for other elements demonstrate that the difference between the two kinds of partition functions is small below 7000 K, but that it rapidly increases above 9000 K. Therefore and in view of the previous section, the values of the partition functions, calculated with the polynomials of de Galan et al. between 5000 and 9000 K, were used to determine the values of A, Band C for the 13 elements labelled t in Table 2. Cu - ATOM

(4 z s? c

6-

O8 2

-2

zu

-4

i? 5-

-6 -6 .I0

c g

\ z 0 E I z 9 E

.I2

4

L

,

,

2

3

4

5

,

,

6

7

,

TEMPERATURE

J

,

9

IO

1xl030

K)

6

I2

II

NI-ATOM

0

d

-8 x

-4

6

-6

i;j \ z

-12

k k

-16

& b

-20

5

-24

25-

-26 202

3

4

5

6

TEMPERATURE

7

6

9

IO

II

(x 1000 K )

Fig. 2. Temperature dependence of partition functions, Z (DF) and Z (ef), for (a) Cu I and (b) Ni I.

1111

Electronic partition functions Table 6. Comparison of partition functions for Cu I: Z (ABC) obtained with the aid of the polynomials of DEGALAN et al. [ 101 and Z (DF) quoted from DRAWIN and FELENBOK[9] T(R)

Z(DF)

2 (AJ.rC)

Rel. error ( ;<)

5429 6599 7276 go22 8844 9750 10750 11852

2.431 2.762 2.986 3.261 3.605 4.050 4.645 5.466

2.427 2.741 2.949 3.202 3.508 3,878 4.328 4.873

-0.18 -0.17 - 1.2 - 1.8 -2.7 -4.2 -6.8 -11

B-u= of the lack of data in the Drawin and Felenbok compjlation, it is impossible to know the validity of the present method for these elements. Therefore it was tested for the partition function of Cu I for which numerical values of the partition function do appear in the work of DRAWIN and FELENBQK [9]. The results are shown in Table 6, in which the values of 2 (ABC) were not calculated with A, B and C in Table 2, but with those obtained by the above procedure. The values of Z (ABC) are smaller than those of 2 (DF), and the difference between the two increases with temperature. This is due to the temperature dependence of Z (a-#) in Fig. 2. It is suggested from Table 6 and similar comparisons for other elements that, for the 13 elements labelled 7 in Table 2, the 2 (ABC)values are by several % smaller than the true values of the partition functions between 8555 and 15 555 K, and by more than several % between 15555 and 12555 K.

4. CONCLULNNG REMARKS Using a method of least squares fit, the electronic partition functions were determined, for the atoms and singly-charged ions of 52 elements, in the form of the second-order polynomials of temperature. The coefficients of the polynomials are valid between 7555 and 12 055 K. The errors for 36 elements (without label in Table 2) are, at most, of the order of lx, and for 13 other elements (labelled t in Table 2) smaller than several % below 15555 K and larger than this above 15555 K. The applied method is useful for obtaining the partition functions in a limited temperature range. Acknowledgements-T& authors express their gratitude to Mr H. University) for his help in the computation.

P. W. J, M. BQUMANS, Theory P. W. J. M.

afSpectrocbemica1

T~IJJI (Osaka

Electra-Communication

Excirution. Hilger & Watts, London, New York (1966). Part 2, Applications and

BOUMANS, Ed., Inductively Coupled Plasma Emission Spectroscopy:

Fundumentals. Wiley, New York (1987). G. HEKZBERG,M~lec~~ Specrru and ~o~~cu~~ Structure & chap. V. V= Nostrand, New York (1945). G. HERZBERG,Molecuiar Spectra and Mol~u~~r Smructurc I, Gap. III. Van Nostrand, New York (195@). C. A. ANDERSENand J. R. HINTHORNE,Anal. Chem. 45, 1421 (1973). H. W. WERNER,Surf. Interface Anal. 2, 56 (1980). W. J. CLMS, Rechn. Astr. Obs. Utrecbt 12,49 (1951). P. W. J. M. BWJMANS, Proc. 9th Coil. Speczr_ Int., Lyon, p. 84 (1961). H. W. DEAWIN and P. FE~E~XK, Data&r Plasmas in L.oc& ~rrn~~~~ ~~u~~&~~~ Gauthier-Villas

Paris (1965). L. DE GALAN, R. SMITHand J. D. WINEFORDNER, Spectrochim. Acta ZJB, 521 (1968). P. W. J. M. BCIUMANS,Spectrochim. Acta 23B, 559 (1968). P. W. J. M. BOUMANS,Excitation of Spectra. Analytical Emission Spectroscopy, Ed. E, L GI~OYE,Vol. 1, Part 2,

Chap. E;,p. 155. Delcker, New York (1972). M. CAPITELLOand G. FERRARO,Snecrro<im.Acfa 3lB. 323 (19%). S. TAMAKIand H. MATSUDA, Sect&i. ion Mass Spectrom. SiMS IV, Ed. A. BENWINGHOVEN, J. OKANO, R. SHIMIZUand H. W. WERNER,D. 85. Snrinaer, Berlin (19841 ~ ’ S. TAMAKI, Mikrochim. Acta III; i (1985). T. KURODA and S. TAMAKI, Mikrochim. Acta (in press).