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The influence of molecular environment on the K-shell fluorescence yield of carbon in small molecules
15 May 1972
CHEMICAL PHYSICS LETTERS
Volume 14, number 2
THE INFLUEIVCE OF MOLECULAR ENVIRONMENT ON THE K-SHELL FLUORESCENCE YIELD OF CARBON IN SMALL
Keceivzd 28 February
MOLECULES
1972
The CTOSSSections for carbon-K X-ray emission have been measured for OS-4 kcV electrons incident on U14, CzH6, C3Hs. CzHz, C2fI4, CO and CO*. It is found that,although the crosss~ctionr per czrbon atom show the SIXI-I~dependence on the incident electron energy, they differ in magnitude by up to 35% This is interpreted 3s ail effect of the molecular environment on the fIuoresccnce yield.
1. Introduction A single vacancy in the K-shell of an atom may dea radiative transition, with the emission
cay by either
of a characteristic X ray, or a non-radiative transition in which an Auger electron is ejected [I] . The fluorescence yield (ok) is defined as the probability that the vacancy is filled by a radiative transition. For light atoms, the fluorescence yields are very smal!; a value of q = 0.0035 for the carbon K-shell has been obtained by Hink and Paschke [a] using a thin graphite target. We have recentIy measured the absolute cross sections for C-K X-ray emission in methane using electron bombardment between 200 eV and 18 keV [3]. By comparison of our data with measurements of Glupe and Mehlhorn [4] for the C-K Auger ejection cross sections in methane, we obtain EL+= 0.0027 for carbon. in this letter we investigate the influence of molecular environment on the value of the fluores-
cence yield, using small gaseous molecules containing carbon.
2. Apparatus and experimenta
procedure
The apparatus hasbeen usedbefore principallyfor the determination of cross sections for the emission of light in the wavelength region of 300-7500 a when electrons are incident oft gaseous targets. An
extensive description is given in ref. [S] . Accordingly, we shali repeat only the main features here. An clectro~~~bearr,, produced by an e!ectron gun mounted
in a high-vacuum
chamber,
is accelerated
to
between SO0 eV and 4 keV and enters a collision chamber through a co~linlati[l~ aperture. The electron current of up to IGO &A is integrated by a precision (O.S%a)integrator. The pressure measurement in the collision chamber (IO-3--iO-3 torr) is made by an MKS Baratron capacitance manometer, which is accurate to about 2%. The contamination of target gases due to air is checked with a n~onochromator by observing an optica! line (39 14 A) of nitrogen. For the gases used here it is not possible to use the liquid nitrogen trap in the collision chamber except for CO and C8,. The X rays are detected at 90” to the incident electron beam by a Sicmcns rype F flow-mode proportional counter with a 6 p Hostaphon (Mylar) window. This has a transmission of about 4% for C-K X rays. P- IO counter gas is used at atmospheric pressure. The pulse height spectrum from the counter is recorded by a ~nuItich3~neI anatyser and the counts are integrated between appropriate upper and lower discriminator levels. * NATO Research Fellow. ** On Ieaw of absence from the Deprtntent ot’Nuc!ixr En~~neer~n~, Kyushu University, Fukuoka, Japnn; Research FcIlow in the Cultural &cement between Japan and the Netherlands.
285
CHEM!CALPHYSfCSLE'iTERS
Volume 14, number 2
The cross section for X-ray emission from each target is evaluated using the following formula:
15May 1972 Table 1
Relative C-K X-ray yields for different molecules, and corrections
ox = (41ilRJ N(Q)@W-j,
(I)
where S(Q) is the detector signnal,measured as a number of X-ray counts corresponding to radiation emitted in the solid angle 22 subtended by the counter; II is the number
of incident
electrons,
N is the target
density, L is the interaction length viewed by the counter and T is the transmission of the window of the counter. It is assumed that the emission is isotropic. The comparison of ox for the different gases has beer! made in the following way: from eq. (I) we see that S(R) is proportional to o,T when al! the data refer to the same gas pressure and integrateti electron current (Q and L are apparatus constants). In these measurements the gas pressure is varied behveen lo-” and 10m3 torr. A linear relation is established between S(0) and the gas density, while the X-ray count rate is kept below 300 counts/set to avoid pile-up of pulses. From the gradient of the S(sZ)-N graphs absolute values of co,rare determined, where c follows from eq. (1) and is the same for all the gases used. In the case of CO and CO,, the bremsstrahlung due to oxygen nuclei is not negligible, but a correction can be made from a subsidiary experiment in which the brcmsstrahlung X rays from a molecular oxygen target are detected. These counts are simply slubtracted from the CO and CO, results after scaling for the same target density of oxygen atoms. The very small contribution of oxygen-K X rays, which are excitec! at incident energies above 540 eV, is subtracted in the same way. At 500 eV for CO, the cor-
rection is about 9% for CO 570, while the bremsstrahlung due to the carbon nucleus itself is about 3% of the characteristic X-ray yield of methane at tfc mamcelectron energy. (This Aue is obtained by scaling from oxygen by Z2, where 2 is the atcmic number of the target nucleus, as indicated by Heitler [6].) The experiments are then repated with two window-foils, in order to measure co,TZ for each gas. From these extra measurements a correction can be made for effects due to selective absorption by the Xray counter window. It is found that between SO0 eV and 4 keV the values of ux for each gas show the same (shape) dependence on eIectron impact energy within the ex-
Gas
for window transmission (‘I?
U,T
0xT2
cJ&wl~&~4)
CH4
1 a00
1.000
C2H6
0.980
0.939
C3He
0.965
0.906
1.03 -c0.08
0.820 0.898 0.654 0.738
0.797 0.889 0.666
0.84+ 0.06 0.91 t 0.07 0.64 2 0.05
0.715
0.76 f 0.06
C2 Hz C2 H4
co CO2
1.00 1.02-c0.08
perimental errors (3%). (T is a constant for each gas.) The X-ray yields with one and two windows are given relative to CH, in columns 1 and 2 of table 1. The numbers in column 1 are proportional to uuT, and those in column 2 are proportional to a,T2, so that the ratios of ux with respect to ox for methane are obtained by taking the quotient of the squares of the mmbers in column I over the numbers in column 2. This procedure approximntely corrects for the slight differences in the transmission of the windows for carbon X rays from different moiecules. These differences are expected as the X-ray energies differ by several eV due to chemical shifts (= S eV) in the molecular energy levels (see for instance, ref. [7] ). However, due to poor resolution of the proportional counter, these shifts cannot be observed directly.
3. Discussion It can be seen that the saturated alkenes CH,, C,H6 and C3H8 have about the same ux value per carbon atom. For CO and CO,, us is definitely lower. The same is true for CqH, and C2Hq (as compared to C2H6).In order to expi& these differences we have to realise that oxis determined
by both the ionization
cross
section of the K-shell, and also by the probability of subsequent radiative decay. Thus, a, can be written as the product of the K-shell ionization cross section ak and the fluorescence yield wk. we think it reasonable to assume that ok for carbon is only sIightIy influenced by its molecular environment because there is only a relatively small chemical shift (= 2%) in its binding energy r/;, (see for example ref. 181) and oki?: is a universal function of EcI/Uk (EeJ is the in-
286 :
_.:.
voiumc14, number
2
CHEMICAL PHYSICS LETTERS
&dent e!ectron energy; see for instance ref. [9])_ The large differences in ox then must be explained by differences in tik_ Such differences are feasible because the radiation matrix elements and Auger transition matrix elements will be dependent on the wavefunctions of the valence-state electrons which differ from molecule to molecule. Also, &a&up and shake-off processes can occur with the K-shell ionization of the mo!ecuies [S} , and these effects may differ frorn mol&xI~@to moIecule; in some cases the motecule b prob8bIy unstabIe. The Same states can also be formed by simultaneous K- and L-ionization or by K-ionization and L;excitation, hut these often have small cross sections when compared to single ionization. It has already been shown that the fluorescence yields of atoms are inff ucnced by outer-shell ionization [ 10,1 I]. Radiation will also be measured from molecules in which the K-eIec:ron is excited to an empty vaIence orbital, and the molecule is not ionized. In conclusion, we note that these n~olccules have aIso been investigated ex~erin~enta!iy by hlattson and EhIert f 121, who studied the spectra of characterjstic carbon X rays at high resolution. Theoretical calculations have been made by Marine, who determined the rciative transition probabilities for different valence electrons in each conl~ound using extended f-fiickel wovefunctions f 131 , and later by CNDOf2 calculations Cunpublished). Our results suggest that the differences in a, for these molecules are connected with ok_ Complcmentary measurements shoutd be made to confirm our a~nInption that the influence of the mo!ecular environment on ok is smaii. 1% should also remark that it would be csefut to study the X-ray spectrum with a window-less detector because some of the emission spectrum may be above the carbon absorption edge in
x5 May 1972
the Mylar window of the proportional counter; however, we estimate that this is only 3 very small fraction.
It is a pleasure to acknuwfedge the technical assistance of i&Q.f. van Zeciand in these experiments, and also the critical comments of Dr. R. Manne and Dr. F.W. Saris. This work is sponsored by F.O.M. with financial support by Z.W.O. References hfak and CR. Swift, Rev. Mod. Phys. 38 (1966) 513. [Z] W. Hink and H. Paschke, Phys. Rev. A4 (1971) 507. [3/ H. Tawnra, K.G. Itanison and F.3. de i-icer, to be pub-
(11 R.W. Fink, R.C. Jopsan, H.
Iished. (41 G. Glupe and W. hlehihorn,
Phys. Letters 2SA (1967) 274, I.51 H.R. hfoustafa. F.J. de Heer and 3. Schuttcn, Physica 40 (1969) 517. I61 5%‘.Heitler, The quantum theory OFradiation (Ckuendon Press, 0.x&d, I954) p. 242. 171 K. Sicgbahn, C. Nordling, G. Johansson, J. tfedman, P.F. &den, K. Namrin, U. C&us, T. Bergmark, L.D. Werme, R. Mzmnc and Y. Baer, ESCA applied to free molecules (North-HoUand, Amsterdam, i969). f8j W.E. Xfoddcman, T.A.CarIson,O. Krause, B.P. Pulien, 5V.E. Butl and G.K. Schweitzer, J. Chem. Phys. 55 (f97f) 2317. [9] L. Vriens, in: Case studies in atomic collision pl~yfics, Vol. I, eds. E.W. McDznicl and M.R.C. lLfcDowel1 (~orth-~~~~a~d, Amsterdam, 1969) p. 335. 1101 F.W. Saris and 13. Ondordelindcn, Physica 99 (t 990) 44t. fi 1 j T-2. barkins, f. Phys. B4 (I97 I) L29. 1121 R-A. Mattson and R.C. Ehtert, 3. Cflem. Whys. 48 (1968) 5465 [13J R. Mannc, J. Chem. Phys. 57 (1970) 5733.
CHEMICAL PHYSICS LETTERS
Volume 14, number 2
THE INFLUEIVCE OF MOLECULAR ENVIRONMENT ON THE K-SHELL FLUORESCENCE YIELD OF CARBON IN SMALL
Keceivzd 28 February
MOLECULES
1972
The CTOSSSections for carbon-K X-ray emission have been measured for OS-4 kcV electrons incident on U14, CzH6, C3Hs. CzHz, C2fI4, CO and CO*. It is found that,although the crosss~ctionr per czrbon atom show the SIXI-I~dependence on the incident electron energy, they differ in magnitude by up to 35% This is interpreted 3s ail effect of the molecular environment on the fIuoresccnce yield.
1. Introduction A single vacancy in the K-shell of an atom may dea radiative transition, with the emission
cay by either
of a characteristic X ray, or a non-radiative transition in which an Auger electron is ejected [I] . The fluorescence yield (ok) is defined as the probability that the vacancy is filled by a radiative transition. For light atoms, the fluorescence yields are very smal!; a value of q = 0.0035 for the carbon K-shell has been obtained by Hink and Paschke [a] using a thin graphite target. We have recentIy measured the absolute cross sections for C-K X-ray emission in methane using electron bombardment between 200 eV and 18 keV [3]. By comparison of our data with measurements of Glupe and Mehlhorn [4] for the C-K Auger ejection cross sections in methane, we obtain EL+= 0.0027 for carbon. in this letter we investigate the influence of molecular environment on the value of the fluores-
cence yield, using small gaseous molecules containing carbon.
2. Apparatus and experimenta
procedure
The apparatus hasbeen usedbefore principallyfor the determination of cross sections for the emission of light in the wavelength region of 300-7500 a when electrons are incident oft gaseous targets. An
extensive description is given in ref. [S] . Accordingly, we shali repeat only the main features here. An clectro~~~bearr,, produced by an e!ectron gun mounted
in a high-vacuum
chamber,
is accelerated
to
between SO0 eV and 4 keV and enters a collision chamber through a co~linlati[l~ aperture. The electron current of up to IGO &A is integrated by a precision (O.S%a)integrator. The pressure measurement in the collision chamber (IO-3--iO-3 torr) is made by an MKS Baratron capacitance manometer, which is accurate to about 2%. The contamination of target gases due to air is checked with a n~onochromator by observing an optica! line (39 14 A) of nitrogen. For the gases used here it is not possible to use the liquid nitrogen trap in the collision chamber except for CO and C8,. The X rays are detected at 90” to the incident electron beam by a Sicmcns rype F flow-mode proportional counter with a 6 p Hostaphon (Mylar) window. This has a transmission of about 4% for C-K X rays. P- IO counter gas is used at atmospheric pressure. The pulse height spectrum from the counter is recorded by a ~nuItich3~neI anatyser and the counts are integrated between appropriate upper and lower discriminator levels. * NATO Research Fellow. ** On Ieaw of absence from the Deprtntent ot’Nuc!ixr En~~neer~n~, Kyushu University, Fukuoka, Japnn; Research FcIlow in the Cultural &cement between Japan and the Netherlands.
285
CHEM!CALPHYSfCSLE'iTERS
Volume 14, number 2
The cross section for X-ray emission from each target is evaluated using the following formula:
15May 1972 Table 1
Relative C-K X-ray yields for different molecules, and corrections
ox = (41ilRJ N(Q)@W-j,
(I)
where S(Q) is the detector signnal,measured as a number of X-ray counts corresponding to radiation emitted in the solid angle 22 subtended by the counter; II is the number
of incident
electrons,
N is the target
density, L is the interaction length viewed by the counter and T is the transmission of the window of the counter. It is assumed that the emission is isotropic. The comparison of ox for the different gases has beer! made in the following way: from eq. (I) we see that S(R) is proportional to o,T when al! the data refer to the same gas pressure and integrateti electron current (Q and L are apparatus constants). In these measurements the gas pressure is varied behveen lo-” and 10m3 torr. A linear relation is established between S(0) and the gas density, while the X-ray count rate is kept below 300 counts/set to avoid pile-up of pulses. From the gradient of the S(sZ)-N graphs absolute values of co,rare determined, where c follows from eq. (1) and is the same for all the gases used. In the case of CO and CO,, the bremsstrahlung due to oxygen nuclei is not negligible, but a correction can be made from a subsidiary experiment in which the brcmsstrahlung X rays from a molecular oxygen target are detected. These counts are simply slubtracted from the CO and CO, results after scaling for the same target density of oxygen atoms. The very small contribution of oxygen-K X rays, which are excitec! at incident energies above 540 eV, is subtracted in the same way. At 500 eV for CO, the cor-
rection is about 9% for CO 570, while the bremsstrahlung due to the carbon nucleus itself is about 3% of the characteristic X-ray yield of methane at tfc mamcelectron energy. (This Aue is obtained by scaling from oxygen by Z2, where 2 is the atcmic number of the target nucleus, as indicated by Heitler [6].) The experiments are then repated with two window-foils, in order to measure co,TZ for each gas. From these extra measurements a correction can be made for effects due to selective absorption by the Xray counter window. It is found that between SO0 eV and 4 keV the values of ux for each gas show the same (shape) dependence on eIectron impact energy within the ex-
Gas
for window transmission (‘I?
U,T
0xT2
cJ&wl~&~4)
CH4
1 a00
1.000
C2H6
0.980
0.939
C3He
0.965
0.906
1.03 -c0.08
0.820 0.898 0.654 0.738
0.797 0.889 0.666
0.84+ 0.06 0.91 t 0.07 0.64 2 0.05
0.715
0.76 f 0.06
C2 Hz C2 H4
co CO2
1.00 1.02-c0.08
perimental errors (3%). (T is a constant for each gas.) The X-ray yields with one and two windows are given relative to CH, in columns 1 and 2 of table 1. The numbers in column 1 are proportional to uuT, and those in column 2 are proportional to a,T2, so that the ratios of ux with respect to ox for methane are obtained by taking the quotient of the squares of the mmbers in column I over the numbers in column 2. This procedure approximntely corrects for the slight differences in the transmission of the windows for carbon X rays from different moiecules. These differences are expected as the X-ray energies differ by several eV due to chemical shifts (= S eV) in the molecular energy levels (see for instance, ref. [7] ). However, due to poor resolution of the proportional counter, these shifts cannot be observed directly.
3. Discussion It can be seen that the saturated alkenes CH,, C,H6 and C3H8 have about the same ux value per carbon atom. For CO and CO,, us is definitely lower. The same is true for CqH, and C2Hq (as compared to C2H6).In order to expi& these differences we have to realise that oxis determined
by both the ionization
cross
section of the K-shell, and also by the probability of subsequent radiative decay. Thus, a, can be written as the product of the K-shell ionization cross section ak and the fluorescence yield wk. we think it reasonable to assume that ok for carbon is only sIightIy influenced by its molecular environment because there is only a relatively small chemical shift (= 2%) in its binding energy r/;, (see for example ref. 181) and oki?: is a universal function of EcI/Uk (EeJ is the in-
286 :
_.:.
voiumc14, number
2
CHEMICAL PHYSICS LETTERS
&dent e!ectron energy; see for instance ref. [9])_ The large differences in ox then must be explained by differences in tik_ Such differences are feasible because the radiation matrix elements and Auger transition matrix elements will be dependent on the wavefunctions of the valence-state electrons which differ from molecule to molecule. Also, &a&up and shake-off processes can occur with the K-shell ionization of the mo!ecuies [S} , and these effects may differ frorn mol&xI~@to moIecule; in some cases the motecule b prob8bIy unstabIe. The Same states can also be formed by simultaneous K- and L-ionization or by K-ionization and L;excitation, hut these often have small cross sections when compared to single ionization. It has already been shown that the fluorescence yields of atoms are inff ucnced by outer-shell ionization [ 10,1 I]. Radiation will also be measured from molecules in which the K-eIec:ron is excited to an empty vaIence orbital, and the molecule is not ionized. In conclusion, we note that these n~olccules have aIso been investigated ex~erin~enta!iy by hlattson and EhIert f 121, who studied the spectra of characterjstic carbon X rays at high resolution. Theoretical calculations have been made by Marine, who determined the rciative transition probabilities for different valence electrons in each conl~ound using extended f-fiickel wovefunctions f 131 , and later by CNDOf2 calculations Cunpublished). Our results suggest that the differences in a, for these molecules are connected with ok_ Complcmentary measurements shoutd be made to confirm our a~nInption that the influence of the mo!ecular environment on ok is smaii. 1% should also remark that it would be csefut to study the X-ray spectrum with a window-less detector because some of the emission spectrum may be above the carbon absorption edge in
x5 May 1972
the Mylar window of the proportional counter; however, we estimate that this is only 3 very small fraction.
It is a pleasure to acknuwfedge the technical assistance of i&Q.f. van Zeciand in these experiments, and also the critical comments of Dr. R. Manne and Dr. F.W. Saris. This work is sponsored by F.O.M. with financial support by Z.W.O. References hfak and CR. Swift, Rev. Mod. Phys. 38 (1966) 513. [Z] W. Hink and H. Paschke, Phys. Rev. A4 (1971) 507. [3/ H. Tawnra, K.G. Itanison and F.3. de i-icer, to be pub-
(11 R.W. Fink, R.C. Jopsan, H.
Iished. (41 G. Glupe and W. hlehihorn,
Phys. Letters 2SA (1967) 274, I.51 H.R. hfoustafa. F.J. de Heer and 3. Schuttcn, Physica 40 (1969) 517. I61 5%‘.Heitler, The quantum theory OFradiation (Ckuendon Press, 0.x&d, I954) p. 242. 171 K. Sicgbahn, C. Nordling, G. Johansson, J. tfedman, P.F. &den, K. Namrin, U. C&us, T. Bergmark, L.D. Werme, R. Mzmnc and Y. Baer, ESCA applied to free molecules (North-HoUand, Amsterdam, i969). f8j W.E. Xfoddcman, T.A.CarIson,O. Krause, B.P. Pulien, 5V.E. Butl and G.K. Schweitzer, J. Chem. Phys. 55 (f97f) 2317. [9] L. Vriens, in: Case studies in atomic collision pl~yfics, Vol. I, eds. E.W. McDznicl and M.R.C. lLfcDowel1 (~orth-~~~~a~d, Amsterdam, 1969) p. 335. 1101 F.W. Saris and 13. Ondordelindcn, Physica 99 (t 990) 44t. fi 1 j T-2. barkins, f. Phys. B4 (I97 I) L29. 1121 R-A. Mattson and R.C. Ehtert, 3. Cflem. Whys. 48 (1968) 5465 [13J R. Mannc, J. Chem. Phys. 57 (1970) 5733.