H. B. FANNIN, J . J . H U R L Y , and F. R. M E E K S * Department of Chemistry, University o[ Cincinnati, Cincinnati, Ohio 45221-0172
Relative populations of excited states of He(I) in reduced-pressure ICPs have been shown to obey Fermi-Dirac statistical counting. A single ther- modynamic temperature--2000 K--defines the distribution. The exper- imental relative populations and the Fermi-Dirac distributions agree within fractions of one percent. Index Headings: Statistical mechanics; Spectroscopic temperature; Fer- mi-Dirac distribution.
INTRODUCTION
De Galan I has presented a cogent summary of theo- retical attempts to account for experimental observa- tions on ICPs up to 1984, reviewing critically the essen- tials of four basic approaches to Ar ICPs and proposing one further model; all the preceding discussions deal with the analytical section of the plasma.
This is the first in a series of studies in which we apply standard statistical mechanics as a first step in account- ing for distribution of excited neutrals, ions, and elec- trons in reduced-pressure He and Ar plasmas, including mixtures; attention is confined to the region within the coil of the ICP. In this first paper we deal exclusively with data on the excited neutral states of He(I).
The methodology begins with the most convenient for- mulation, the Grand Partition Function, and proceeds to account in excellent fashion for the observed relative populations of excited He neutrals in the ICP. Impor- tantly, one is required only to note that all species share a common thermodynamic temperature when the system is either at equilibrium or in a stationary state. In this assertion we do not depart from the implicit assumption made by all workers who invoke, for example, the Boltz- mann relation ("distribution") or its extension, the Saha relation. Clearly, the notion of a temperature common to all components of a mixture does not disallow the possibility of fluctuations in temperature.
The model, then, consists of an assembly of atoms in various states of excitation from the ground state up to some value short of the ionization potential. The data to which the treatment is applied do not include all possible states, because of instrumental limitations. Even so, the correlation of relative populations with those arrived at statisticomechanically is very good indeed. Approxi-
Received 25 April 1988. * Author to whom correspondence should be sent.
mately 30 transitions for He(I) in the near-UV-visible spectrum were recorded and analyzed.
MATHEMATICAL FRAMEWORK
In both notation and sequence this section generally follows Rice? That electrons in atoms m u s t obey Fermi- Dirac statistics can be traced to early papers by Fermi 3 and to the standard works of Pauling and Wilson 4 and Leighton, 5 among many others.
Below is presented an application of Fermi-Dirac sta- tistics which is, to use de Galan's term, "tutorial"-- in deference to the reader whose temporal separation from a course in statistical mechanics may perhaps be long.
The Grand Partition Function (GPF), for Fermi-Dirac counting is
(GPF) = ~r,[1 + )~iexp(-~, /kT)] -1
where ei is the energy of the ith state; k is Boltzmann's constant; T is absolute temperature; and },i = e x p ( t t J k T ) , where tt~ is chemical potential. The choice of GPF for the problem is made since the He(I) atoms in the plasma can be treated as independent subsystems, s Collisions, when microscopic reversibility is in effect, do not affect the thermodynamic properties. Ordinarily the subscript on tt~ is omitted; it is included here for reasons which will appear below.
Because the total number of particles, N, is given by
N = Y,~w,{1 + exp[(Ei- #~)/kT]} -1 (1)
it can be inferred 2 that since N = Z~n~, the population n~ of the ith state is in fact the ith term in the sum in Eq. 1. For electrons, a factor w~, equal to two and different from the orbital degeneracy g~, must be introduced into Eq. 1 to represent spin degeneracy, so that finally
n~ 1 (2)
wi 1 + exp[(e~ - t t i)/kT] "
The formal symbol w~ rather than its numerical value is temporarily retained for generality. Equation 2 gives the number of "particles" (electrons) per state in a he- lium atom for the energy ei. Alternatively, it can be in- terpreted as the probability of occupation of the ith state. Equation 1, an implicit function of tt~, defines tt~. Thus both Eqs. 1 and 2 are required in order to describe an assembly of electrons such as those in a neutral atom.
The behavior of nJw~ vs. Ei is as shown in Fig. 1, where
FIG. 1A. Schematic of Fermi-Dirac distr ibution function for a ground- state atom where tt 0 is the Fermi level.
we indicate go instead of gi. When ez = go, nJw~ = 1/2; since w~ = 2 for electrons, n~ = 1. T h a t is, the populat ion of the i th state is unity. Since by the Pauli Principle the occupat ion index of all states below and including the highest occupied one is uni ty for the ground state of an atom, the heavy lines in Fig. 1A represent the electron dis tr ibut ion for an a tom in its ground state. All states below go are associated with one electron, and all states above go are unoccupied. For an excited atom, the smooth curve in Fig. 1B represents the occupation indices. For q < go the dis tr ibut ion is "concave downwards" (second derivative negative) and for ei > go it is "concave up- wards" (second derivative positive). The second deriv- ative of nJwi with respect to Ei is, for a given go and T,
[ 52(ni/---wi)] - (ni/wi) 1
~i 2 J~o,r k T2
• (1 - n , / w , ) ( 2 n , / w i - 1) (3)
where 0 < nJwi < 1/2. Clearly the second derivative is zero for ei = go (a point of inflection in the distr ibution) and negative for e~ < go. For e~ >> go the Fermi-Dirac funct ion reduces to the Boltzmann:
n i / w i = [exp(go /kT)][exp( -Ei /kT) ]. (4)
The second derivative of the Bol tzmann form, Eq. 4, is
ni/wi
To Ground State 1.0
- ~ Translator y Electrons 0.5 Excited Neutrals ~ and
Positive Ions
0.0 IP /
I 11' I I
180000 190000 200000 210000 220000 Upper State Energy (cm-1)
FIG. lB. Schematic of Fermi-Dirac distribution function for He at 2000 K. IP denotes first ionization potential for He (198,305 cm -1) and is regarded as tt o.
~2(ni/wi) n, = - - (3a)
&i 2 (kT) 2 '
clearly a positive value. The concavity (upwards or down- wards) of a plot of populat ion vs. ei for a given experi- menta l system thus determines whether the subsystems (electrons, ions) behave according to Fermi-Dirac or Bol tzmann statistics. (Bose-Einstein counting, a th i rd possible dis tr ibut ion function, is unlikely to be encoun- tered in a plasma; the suggestion of distr ibutions other than Boltzmann, Fermi-Dirac, and Bose-Einstein can be discounted2) We conclude definitively tha t for a fixed value of T and go the Fermi-Dirac behavior is to be ex- pected when q < go and tha t Bol tzmann behavior is to be expected when e~ >> go- The region beyond go repre- sents the well-known "blending" of the Fermi-Dirac dis- t r ibut ion into the Boltzmann.
A slight complication arises when one is considering excited states of atoms, however. While, for example, go is by definit ion a constant (the "Fermi level") in the successful free-electron-gas theory of metals, it is so be- cause the volume is taken as constant and go is inversely dependen t upon V through conversion of Eq. 1 into an integral (Eq. 3):
rod ~ ~ W de N = 4~rV(2m/h2) a/2 1 + exp[(e - g) /kT] " (5)
In Eq. 5 m is electron mass and h is Planck's constant . (For details of the dependence of g on V see Ref. 2; the result is not obvious from inspection of Eq. 5.)
For neutra l atoms, increasingly more highly excited states have increasingly larger "volumes." I t is therefore to be expected tha t for each gi there is a corresponding V~. This is made discernible by subscripting the V in Eq. 5 and following through Rice's t rea tment .
For excited neutrals, then, there exists a slightly dif- fe rent gi for each ei, and gi shifts to the left in Fig. 1B as e~ increases.
I t is clarifying to establish the connect ion between nil w~ and gi. This is easiest to do by forming the part ial derivative of nJwi with respect to g~ at fixed e~ and T, as follows: Le t X = (el - g i ) /kT; then
[ 5(n,/w,)] 1 - - - ~ # ~ J,,.T = ~-~[1/(1 + e')]
• [1/(1 + e- ' ) ] . (6)
Now the produc t on the r ight-hand side of Eq. 6 is just the mean-square deviat ion of the populat ion of the i th state:
ai 2 = ( ( n l / w i ) 2) - - ( n i / w i ) e
= [1 / (1 + e 0 1 1 1 / ( 1 + e - 0 1 . (7)
When X >> 1, zi 2 -* e x p ( - X ) = exp[ - ( e i - gi)/kT] = i e x p ( - e i / k T ) .
For X = 0, zi 2 -~ 0.25. For X << 0 the limit is the same as in Eq. 7, due to the algebraic symmet ry of the produc t of reciprocals on the r ight-hand side of Eq. 7. I t is clear then tha t the popula t ion ni/wi is insensitive to gi for large differences (compared to k T ) between e~ and gl, bu t most sensitive to tt i when E~ and g~ most nearly coincide.
1182 Volume 42, Number 7, 1988
TABLE I. 100% He(I).
P = 4.67 Torr rf Power = 100 W A = 1900 T = 2000 K
The preceding evaluat ion of f luctuations refers to a system in thermodynamic equil ibrium. In a state near to equi l ibr ium (for example , a stationary state) the same considerations hold true to the extent that the various quantities involved (T, ~i, etc.) in calculation of the fluc- tua t ions also remain valid. More specifically, if the t ime derivatives of the equ i l ib r ium- the rmodynamic quan- tit ies are zero or negligible, then the above assertions can be taken as true. In the end, it is the degree of accord with available experimental data which m u s t be em- ployed as the test for validi ty of use of equi l ibr ium con- cepts and calculations, i.e., for microscopic reversibili ty.
The effective volume V~ can be calculated f rom Eq. 5 for T = 0 (see Ref. 2). V~ is not the atomic volume bu t rather the volume of a spherical shell corresponding to the eigenvalue ei and therefore to the corresponding or- bital. Integration at T = 0 for wi = 2 (g = 2 in Ref. 2) provides
N = (81rV/3)(2rn#i /h2) 3/2. (5a)
Since N = 2 for He(I) ,
Vi = 8.76 x 10-16/p.i3/2 (8)
where #i is expressed in cm -1. I t is easy to show--although not within the range of interest of this paper--that al- though Eq. 5a is obtained for T = 0, the result is insig- nificantly different from that which would result at T = 2000 K; in fact the temperature would have to be of the order of magnitude of one million degrees before the error in Eq. 5a became significant)
TABLE II. 100% He(I).
P = 38.5 Torr rf Power = 100 W A = 150 T = 2000 K
~i gl Ri (nl/w,) ttl Vi % Dev.
184865 1 NA a NA NA NA NA 190940 1 6.19E+01 4.13E-01 190449 3.467 - 8 . 0 8 E - 0 2
The ICP relative populations for He(I) are based upon data taken by one of us (H.B.F.), some discussion of which has already occurred in this journal 9,1°,n but with- out the involvement of statistical mechanics.
The experimental apparatus and conditions have al- ready been described in Refs. 9, 10, and 11.
In Tables I-IV are given upper-state energies (~i), cor- responding eigenstate degeneracies (gz ÷ wi), relative populations (Rz), theoretical relative populations (nJwi), chemical potentials (#z), effective state volumes (V~), and a measure of agreement of the experimental populations with the theoretical ( % Dev.). The pressure (P), rf power, conversion factor A (defined in the following section), and temperature (T = 2000 K for all data) are given in the heading of the tables. The slit area was in each case of the order of magnitude of i × 10 -7 m 2. The pressure indicated is the average of two pressures: P = (Pin + Pout)/2, where "in" and "out" refer to the torch.
Estimates of experimental errors have been made in Refs. 9, 10, and 11.
C A L C U L A T I O N S
The Einstein relations connects relative populations Ri with relative intensity Ii, wavelength Xi, degeneracy gi, and Einstein emission coefficient A~j:
w h e r e R~ is t h e n u m b e r of p h o t o n c o u n t s p e r s e c o n d for t h e i -~ j e m i s s i o n a b o v e t h e c o n t i n u u m . I f t h e p o p u l a t i o n of t h e i t h s t a t e were d e t e r m i n a b l e a b s o l u t e l y i t w o u l d be p o s s i b l e to w r i t e R~ = nJwi , w h a t e v e r t h e f o r m of t h e s t a t i s t i c o m e c h a n i c a l d i s t r i b u t i o n r e p r e s e n t e d b y ni/wi. B u t s ince t h e R~ a re r e l a t i v e va lues we m u s t w r i t e
Ri = IiXi/giAij (9)
w h e r e A is a p r o p o r t i o n a l i t y f ac to r s u m m a r i z i n g i n s t r u - m e n t a l a n d o p t i c a l g e o m e t r i c effects . Ri is e x p e r i m e n t a l l y d e p e n d e n t u p o n E~, as is nJwi; t h e y b o t h have t h e s a m e s lope ( and t h e r e f o r e t h e s a m e shape ) w h e n p l o t t e d a g a i n s t
~i" E q u a t i o n 2 is c o m b i n e d w i t h Eq. 9 in o r d e r to e s t a b l i s h
t h e ui in t h e f i f th c o l u m n of each t ab l e :
Ri = A{1 + exp[(e~ - ui) /kT]} -1. (10)
E q u a t i o n 10 is e x a c t l y eq. 1.17, in c h a p t e r 14 o f Ref. 2, w i t h a d i f f e r e n t choice o f symbo l s . H e r e , i d e n t i f i c a t i o n of ui c o r r e s p o n d s to i d e n t i f i c a t i o n of a in t h a t source . I d e n t i f i c a t i o n of u~ for e a c h Ri a n d e~ c o n s t i t u t e s a f i t o f t h e e x p e r i m e n t a l d a t a to a F e r m i - D i r a c d i s t r i b u t i o n .
Vi is o b t a i n e d f r o m Eq. 8 o f t h i s work , a n d t h e c o l u m n h e a d e d "% Dev . " r e su l t s f r o m e v a l u a t i o n of t h e q u a n t i t y [1 - A(ni/wi)/Ri] x 100 for e ach ei. I t is a m e a s u r e of t h e deg ree of f i t b e t w e e n Ri a n d nJw~.
E s t a b l i s h i n g t h e t e m p e r a t u r e was a r e l a t i v e l y s i m p l e t a sk . A b e s t - f i t cu rve d r a w n t h r o u g h t h e d a t a for each
e x p e r i m e n t l ed to t h e o b s e r v a t i o n t h a t t h e L a n g e v i n F u n c t i o n L ( y ) , w h e r e y = (ei - I P ) / k T , c o i n c i d e d a l m o s t e x a c t l y w i t h t h e d a t a . S ince
L ( y ) = c o t h y - y-1 = F(~i, T) , (11)
i t was ea sy to show t h a t t h e v a l u e T = 2000 K p r o v i d e d t h e b e s t fit. 1~ (A p o w e r se r ies f i t as wel l c o u l d have b e e n used . ) T h e L a n g e v i n m e t h o d is a p p r o p r i a t e b e c a u s e i t s s l ope vs. ei co inc ide s e x a c t l y w i t h t h a t o f t h e F e r m i - D i r a c f u n c t i o n nJw~ w h e n T = 2000 K a n d u~ is as s h o w n in t h e t ab l e s . V a r i a t i o n of T b y 100 K or so d e s t r o y s t h e f i t a p p r e c i a b l y . S u b s t i t u t i o n o f 2100 K for 2000 K a t ei = 191,493 c m -1 in t h e t a b l e g e n e r a t e s a n e r r o r o f 14% in nJwl a n d an e r ro r o f - 1 6 % in t h e l a s t c o l u m n of T a b l e I, t h e l a t t e r to be c o m p a r e d to t h e l i s t e d e r r o r of ~ 0 . 0 8 % . T h e a c c o r d b e t w e e n Ri a n d n~/wi is t h e r e f o r e q u i t e sen - s i t ive to T.
D I S C U S S I O N
T h e r e d u c e d - p r e s s u r e H e I C P is a n i n t e r e s t i n g i f d i f - f i cu l t choice w i t h w h i c h to o p e n a se r ies of s t u d i e s o f t h e s t a t i s t i c a l m e c h a n i c s of p l a s m a s , in p a r t b e c a u s e of t h e l a rge s e p a r a t i o n b e t w e e n g r o u n d - s t a t e e n e r g y a n d t h e e x c i t e d n e u t r a l s t a t e s , a n d in p a r t b e c a u s e of t h e p a u c i t y of e l e c t r o n s in t h e a t o m . I n a l i t e r a l ( i f o l d - f a s h i o n e d ) m o d e l o f e x c i t a t i o n in w h i c h t h e two e l e c t r o n s a r e as- s u m e d to c o r r e l a t e w i t h B o h r o r b i t s i n c r e a s i n g in r a d i u s as ~i inc reases , a d e c l i n i n g d e n s i t y o f s t a t e o c c u p a t i o n resu l t s . T h e ef fec t of t h i s is to i n c r e a s e t h e " v o l u m e " o f t h e s p h e r i c a l she l l in w h i c h t h e e x c i t e d e l e c t r o n s a r e
1184 Volume 42, Number 7, 1988
"located" and thereby to decrease/~ in accord with Eq. 5a.
The decrease in density of state occupation, when ex- treme, produces a blending of the Fermi-Dirac function into the Boltzmann: that is, when the absolute value of ni/w~ becomes very small, Eq. 2 becomes identical with Eq. 4. From relative values of the occupation indices (column four of each table) it is impossible to discern when this change in character of the distribution occurs.
Only from the concavity of the plot in Fig. 2 can it be concluded that for all states observed the correct distri- bution function is the Fermi-Dirac. This is confirmed by contrasting the signs of the second derivatives: Eq. 3 for the Fermi-Dirac and Eq. 3a for the Boltzmann. Note that the sign of the second derivative in Eq. 3 changes from negative to positive only when nJwi -< 1/2; this, however, occurs at e~ -/~o, where Zo is to be taken as the ionization potential, IP. At IP, a phase change--ioniza- t ion-occurs , and for any energy E~ >> IP the distribution is Boltzmann, because a major part of the energy of He(II) and the free gaseous electrons is translatory. Translatory states are effectively a continuum, and hence an ex- tremely low ratio of number of particles to number of accessible states results. Since no He(II) emission was observed in the present study, a detailed calculation of state densities and electron densities beyond the IP can- not be presented at this time; however, they will be given in a succeeding paper dealing with the reduced-pressure Ar ICP, where Ar(II) is observed and discussed.
For each series of a given degeneracy g~ in the tables, z~ is seen to vary (albeit only slightly) with e~. In Table I, for example, for g~ = 3, the average value of #i is 186,064 cm -1 for a change in ei of 10,750 cm -1. That is, the RMS deviation in/~ is approximately 8 % of the change in e~ and is ~0.5% of the average of #~.
More interesting is the variation in V~ with increasing e~, in that V~ can be taken to represent a lessening of occupation index with increasing e~. The first entry in each degeneracy series of the tables is a calibration for the proportionality factor A and can be disregarded. Equation 1 requires use of all accessible state energies e~ in order to evaluate #~ exactly. In these experiments no observations were made on states for principal quan- tum numbers of less than three or greater than ten, and hence the first observed state is regarded as a "pseudo" ground state. The nJwi in the tables would be smaller were these lower states included. The states of high prin- cipal quantum number (small nJwi) contribute very weakly to Eq. 1, i.e., to the identification of z~. Were the absolute populations of the ground and all higher states measured, the sum of the n~/w~ column for all degener- acies would have to be one, since N = 2 for He. This circumstance emphasizes that, while the form of the dis- tribution is correct, i.e., Fermi-Dirac, for neutral excited states of He, the populations are relative to one another, as noted earlier.
CONCLUSIONS
The distribution of relative state populations for ex- cited He(I) is Fermi-Dirac in form, as might have been anticipated from the Pauli Principle as well as the "phys- ical" analogy between an isolated atom and a metal at 0 K in the free-electron-gas theory of metals. Only a single
Ln Ri 8
6
2
IP
o l
i i
190000 195000 2 0 0 0 0 0
Upper State Energy cm-1 FIG. 2. Plot of experimental relative populations of He(I) for 1po series (Table I, g = 3) (circles); solid curve is the corresponding Fermi-Dirac distribution.
2 185000
temperature, 2000 K, is required in order to correlate experimental relative populations with the Fermi-Dirac distribution function for fermions (electrons). No de- tailed physical or kinetic model needs to be invoked in order to establish this correlation, a consequence of the fundamental hypotheses of statistical mechanics.
In several of the papers cited in Ref. 1 (as well as elsewhere in the literature of plasmas 1~) "electron and ion temperatures" as high as 64,000 K, but more usually ~6000-11,000 K, are claimed. Such values cannot logi- cally represent thermodynamic temperatures but serve primarily to reflect the form of the statisticomechanical distribution attempted, and they even depend upon the portion of the experimental curve examined. In an as- sembly of "particles" of different identities--neutrals, ions, and electrons--there can be only one meaningful thermodynamic temperature, and it is inconsistent to imagine that there is a translatory temperature associ- ated with the motion of atoms and yet another "tem- perature" associated with the electrons which the atoms contain. All species in an assembly must be at the same temperature, although different species can obey differ- ent distribution functions.
It is difficult for the present authors to discern how the term LTE ["local thermodynamic (or thermal) equi- librium"] has managed to insinuate itself into the sta- tistical thermodynamics of plasmas. LTE is a nonequi- librium-thermodynamic concept which serves loosely to permit the use of equilibrium-thermodynamic functions (variables and equations) in a small region of a system in which these functions are nonetheless known to be changing in time. LTE is merely another way of indi- cating that gradients of these functions exist. When spec- troscopic intensity measurements are made on a fixed region of a plasma and are found to be invariant with time, then the microscopic phenomena which lead to this time invariance can also be regarded as themselves either in a state of equilibrium or else in a stationary state. In the latter instance it is the duty of the theoretician to detect those properties which are invariant with time, and we feel that it has been convincingly shown that the state distribution of electrons in He(I) is one of them. Further papers in this series will extend and deepen this viewpoint.
APPLIED SPECTROSCOPY 1185
1. L. de Galan, Spectrochim. Acta 39B, 537 (1984). 2. O. K. Rice, Statistical Mechanics, Thermodynamics and Kinetics
(Freeman and Co., New York, 1967), Chap. 14. 3. E. Fermi, Z. Physik 36, 902 (1926). 4. L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics
(McGraw-Hill, New York, 1935), pp. 219-221. 5. R. B. Leighton, Principles of Modern Physics (McGraw-Hill, New
York, 1959), p. 350. 6. T. L. Hill, An Introduction to Statistical Thermodynamics (Ad-
dison-Wesley Publishing Co., Reading, Massachusetts, 1960), Chaps. 7 and 22.
7. O. W. Greenberg and A. M. L. Messiah, Phys. Rev. 138, Bl155 (1965), and references therein.
8. W. Band, An Introduction to Quantum Statistics (D. van Nostrand Co., New York, 1955), p. 156.
9. D. C. Miller, H. B. Fannin, P. A. Fleitz, and C. J. Seliskar, Appl. Spectrosc. 40, 611 (1986).
10. H. B. Fannin, D. C. Miller, and C. J. Seliskar, Appl. Spectrosc. 41, 173 (1987).
11. H. B. Fannin, C. J. Seliskar, and D. C. Miller, Appl. Spectrosc. 41, 621 (1987).
12. H.B. Fannin, Doctoral Dissertation, University of Cincinnati (1988). To be available on microfilm. Extensive details of the fit are given.
13. Inductively Coupled Plasma Emission Spectroscopy--Part 2, P. W. J. M. Boumans, Ed. (John Wiley and Sons, New York, 1987), Chaps. 9 and 10, but especially Sec. 10.5.
Surface-Enhanced Raman Spectroscopy in the Near-Infrared
D. B. CHASE* and B. A. P A R K I N S O N Central Research & Development Department, Du Pont Experimental Station, Wilmington, Delaware 19898
Near-infrared Raman spectroscopy has been used to obtain Surface- Enhanced Raman Spectra (SERS) of pyridine on both silver and gold electrodes. The enhancement factor is higher than that found for visible excitation, and the band intensities are somewhat different. There is no indication of photochemical damage or change of the sample when near- infrared radiation is used, even at relatively high power levels.
Index Headings: FT-Raman spectroscopy; SERS.
I N T R O D U C T I O N
The discovery of Sur face-Enhanced Raman Scatter ing (SERS) more than ten years ago has led to a large amount of research in an a t t emp t to define the basis for the enhancement and the extent of the effect2 SERS has been well documented for (suitably roughened) silver, gold, and copper surfaces when i r radiated with visible wavelength lasers. There are several theories which pur- por t to explain the enhancement mechanism in terms of electromagnetic effects, chemical interactions, ad-a tom mechanisms, or combinat ions of all three. 2 A complete theory should explain the wavelength dependence of the effect, since it is known that , for silver, enhancement is seen with green i l lumination, while for gold and copper, red lasers are necessary. The recent deve lopment in near- infrared Raman spectroscopy using Fourier t ransform techniques 3 provides the capabil i ty to extend the wave- length range for studies of this effect. Using this ap- proach, we have successfully obta ined SERS spectra for pyridine adsorbed on gold and silver electrodes 4 suitably roughened by an electrochemical oxidat ion-reduct ion cycle. This approach has the advantage tha t near-in- f rared radiat ion is less likely to cause photochemical changes in the sample, since the photon energy is quite low. In addition, it extends the wavelength range for obtaining da ta on the enhancement factors which should be useful for fur ther ref inement of the theories concern- ing the mechanism of enhancement .
Received 18 April 1988. * Author to whom correspondence should be sent.
E X P E R I M E N T A L
All spectra were obta ined with the use of a Bomem DA3.02 in ter ferometer operat ing at 2-cm -1 resolution. Fur the r details concerning the descript ion of this in- s t rument can be found in Ref. 5. A nine ty degree off-axis ellipsoidal mirror (Harrick Scientific) was used to collect the scat tered radiat ion in a 180 degree back-scat ter ing configuration. A Spect ron SL50 Nd:YAG laser was used to supply 125 mW of 1064-nm radiat ion to the sample. One hundred scans were averaged, to enhance the signal- to-noise ratio. The electrochemical cell contained a ~ 5- ram-diameter disc electrode of gold or silver, which was prepared by polishing with successive grits of alumina (1, 0.3, and 0.05 #m) followed by an ultrasonic rinse with t r iply distilled water. The cell was then filled with an aqueous 0.05 M pyridine, 0.5 M LiC1 solution. To rough- en the electrode, we swept the potent ia l f rom - 0 . 6 V to 0.2 V relative to Ag/AgC1 for silver and - 0 . 6 to 1.5 V for the gold electrode. Spectra were recorded at several points across the surface, and the peak intensities agreed to
I , I , I , I , I
500 800 1100 1400 1700 CM-I
FIG. 1. FT-Raman spectrum of a pyridine/Au electrode at -0 .6 V versus Ag/AgC1 0.05 M pyridine, 0.5 M LiC1 before roughening.
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