Anal. Chem. 1995, 67, 3782-3787
Quantitative Aspects of FT-lR Emission Spectroscopy and Simulation of Emission-Absorption Spectra Gabor Keresztury,**tJdnos Mink,**@ and J h o s Kristofl Central Research Institute for Chemistry, Hungarian Academy of Sciences, P.0. Box 17, H- 1525 Budapest, Hungary, Department of Analytical Chemistry, University of Veszprem, P.O. Box 158, H-8201, Veszprem, Hungary, and Institute of Isotopes, Hungarian Academy of Sciences, P.0. Box 77, H- 1525 Budapest, Hungary
Recent advances in ET-IR emission spectroscopyof solids are briefly reviewed, and some neglected points conceming the measurement of blackbody radiation are dealt with. A corrected equation describing the single-beam emission spectra is given, taking into accountthe possible thermal radiation of the detector. Similarities between the effect of self-absorptionand that of “illegal” data manipulations on emittance spectra are pointed out, both giving rise to spectral distortions like inverted or split peaks or altered band shapes and intensities. To avoid some of these problems, the use of a linear emission intensity scale, emissivity, is advocated, especially for quantitative work. A special case of self-absorption, namely, that of multilayer samples, is discussed, in which the spectral distributions of emitted and absorbed radiation are signitlcantly Merent. Simulationsof the emission-absorption spectra observed in such cases are shown to help with spectral and strucwal interpretation. With the proliferation of modem FT-IR instruments in the last two decades, an increasing number of laboratories turned to infrared emission spectroscopy (IRES) as an alternative spectroscopic technique for condensed materials and bulk, opaque samples for which transmission or reflection techniques proved to be inadequate. Following the pioneering work of Low and Coleman,’S2some basic considerations and exploratory measurements were published by G r i f t i t h ~ and ~ , ~ Chase5 to test the capabilities and limitations of IRES using IR interferometry. More recently, several other workers checked the influence of sampling conditions (such as sample thickness and temperature, geometry of sample arrangement, etc.) on the quality of IR emission spectra, essentially confirmingthe earlier results. The prime objective of these works, surveyed by Chalmers and Mackenzie; was to develop solid sampling techniques and methods that would ’ Central Research Institute for Chemistry, Hungarian Academy of Sciences. Department of Analytical Chemistry, University of Veszprem. Institute of Isotopes, Hungarian Academy of Sciences. (1) Low,M. J. D. Nature 1965,208. 1089-1099, (2) Low, M. J. D.; Coleman, I. Spectrochim. Acta 1966,22, 396-376. (3) Griffiths, P. R Appl. Spectrosc. 1972,26,73-76. (4) Griffiths, P. R A m . Lab. 1975,7, 37-45. (5) Chase, D. B. Appl. Spectrosc. 1981,35,77-81. (6) Chalmers, J. M.; Mackenzie, M. W. In Advances in Applied Fourier Transform Infrared Spectroscopy; Mackenzie. M . W., Ed.; Wiley: New York, 1988 pp 105-188.
3782 Analytical Chemistry, Vol. 67, No. 20, October 15, 1995
produce good quality spectra free from the known inherent spectral distortions. It has been noted repeatedly that IR emission spectra of condensed samples often suffer from severe distortions (mainly in the regions of strong emission bands) that could be attributed either to surface reflectivity or to self-absorpti~n.~,~-~ To eliminate band distortions due to selective reflection, the use of thick (opaque) samples as reference has been proposed by Rytter and co-worker~.~J~ Another recent major advancement in IRES sampling technique is the application of transient heating11J2of the sample surface in order to get rid of self-absorption and to increase spectral contrast in the case of bulky samples by means of exciting only a thin surface layer temporarily. Most recently, the feasibility of measuring IR emission spectra of highly opaque solids by modulated emission spectroscopywas demonstrated by Guillois et al.I3 Less attention has been paid to practical aspects of FT-IR emission spectroscopy in relation to the fundamental theory of thermal radiation (e.g., measurement of sample temperatu~-e’~J~) and to the presentation (choice of intensity scale) and data processing of emission spectra. The main aims of this paper are to clanfy some key issues that have created controversy or have been glossed over in the literature and to advocate the use of a linear intensity scale, emissivity, for quantitative work. In addition, we would like to draw attention to potential sources of spectral distortions or errors in quantitative applications stemming from improper operations over emittance spectra. It will also be shown on an example that, in special cases, one can take advantage of self-absorption,for instance, to detect the formation of a layered structure on the basis of interpreting the spectrum as an emis sion-absorption spectrum. (7) Kember, D.; Sheppard, N. Appl. Spectrosc. 1975,29,496-500. (8) Willis, H. A; Sheppard, N.; Chalmers, J. In 7th International Conference on Fourier Transform Spectroscopy; Cameron, D. P., Ed. Proc. SPIE-Int. SOC. Opt. Eng. 1989,1145,431-432. (9) Hvistendahl. J.; Rytter, E.; Oye, H. A Appl. Spectrosc. 1983,37, 182-187. (10) Rytter, E. Spectrochim. Acta 1987,43A,523-529. (11) Jones, R. W.; McClelland, J. F. Anal. Chem. 1989,61,650-656. (12) Jones, R. W.; McClelland. J. F. Anal. Chem. 1990,62, 2074-2079. (13) Guillois, 0.; Nenner, I.; Papoular. R; Reynaud, C. Appl. Spectrosc. 1994, 48,297-306. (14) DeBlase, F. J.: Compton, S. Appl. Spectrosc. 1991,45,611-618 Erratum, 1991,45,1209. (15) Keresztury, G.; Mink, J. Appl. Spectrosc. 1992,46,1747-1749.
0003-2700/95/0367-3782$9.00/0 0 1995 American Chemical Society
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Wavenumber (cm-') Flgure 1. Comparison of Planck functions given in wavenumber representation (/-/(:, T), solid lines) with those in wavelength representation
(/-/(A,T ) , broken lines) for three different temperatures. EXPERIMENTAL SECTION
Infrared emission and emission-absorption spectra were measured with a Bomem ME102 spectrometer equipped with a mU;S detector. The emission accessory attached to the side port of the instrument consisted of a sample holder (an electrically heated, polished stainless steel plate) and an off-axis paraboloid mirror to collect the radiation. Double beam emittance or emittance-transmittance spectra were obtained by ratioing the singlebeam emission spectrum of the sample against that of a blackbody reference (a metal plate painted with matte black paint) recorded at identical conditions. Spectral simulations were performed either on a Nicolet 1180 computer (programmed in Fortran) equipped with a Zeta Series 100 digital plotter or on IBM PCs. RESULTS AND DISCUSSION Theoretical Background, with Modifications. Blackbody
Radiation: Wavenumber us Wavelength Representation. The fundamental law governing thermal emission is expressed by Planck's distribution function, H, which describes the spectral radiance (or spectral density of radiant power, often designated as 4) of a blackbody at absolute temperature T. This function is given in textbooks (see, e.g., refs 16-18) and review papers on IRES14J9b20 in various (often erroneous) forms, either as a function of wavelength, A, or frequency, v, or as a function of wavenumber, t, For the sake of completeness, we present here all three mutually consistent forms that give the radiant power emitted from (16) Goody, R M.; Yung, Y. L Atmospheric Radiation: Theoretical Basis 1;Oxford University Press: New York, 1989;pp 29-33. (17)Lenoble, J. Atmospheric Radiative Transfir; A. DEEPAC Publishing: Hamp ton, 1993. (18) Schrader, B., Ed. Infrared and Raman Spectroscopy. Methods and Applications; VCH: Weinheim, 1995. (19)Bates, J. B. In Fourier Transform Infrared Spectroscopy; Ferraro, J., Ed.; Academic Press: New York, 1978 Vol. 1, pp 99-142. (20) Huong, P. V. In Advances in Infrared and Raman Spectroscopy; Clark, R J. H., Hester, R E., Eds.; Heyden: London, 1978 Vol. 4, Chapter 3,pp 85-
107.
a unit area, per solid angle, in elementary spectral intervals CU, dv, and dt, respectively:
H(A,T) CIA = 2 h ~ ~ { ~ ~ [ e x p ( h-cI/ I~Ik- CIA ~)
(1)
H(v,T) dv = 2 h ~ - ~ v ~ / [ e x p ( h v / k-T11-1 ) dv
(2)
H(F,7) d e = 2hc2F3/[exp(hcF/k7)- l]-' dG
(3)
where h, c, and k are universal constants. The inclusion of spectral elements CU, dv, and d t in these equations ensures the correct conversion between the various expressions of spectral radiance. (Note also that versions of the Planck function containing a factor 8n instead of 2 in the above equations refer to radiance in the whole solid angle.) In practical applications of the Planck function in IRES, however, it is not so much the constant factors but the general form of the function that must be chosen properly. Figure 1 shows the two most often used functions corresponding to eqs 1 and 3 for three different temperatures, plotted in a common linear wavenumber scale for easy comparison. It is quite apparent that they describe curves of essentially different shapes, with their maxima shifted considerably to higher wavenumbers in the case of the wavelength representation. This becomes well understandable if we consider the curves described by eq 1 as spectra scanned with a spectral slit width constant in wavelength (A) and the curves described by eq 3 as spectra scanned with a spectral slit width constant in wavenumber (t). Due to the relation &/ = d t / t z (derived from A = 1/t), a spectral slit width constant in wavelength (CU) means an increasing spectral interval in the wavenumber scale (dc) with decreasing wavenumbers. Thus, the integral of the two curves (the total energy detected) in the whole spectrum will be the same for both representations,in accordance with the Stefan-Boltrmann law. The intensity scales of the two series of curves in Figure 1 are arbitrary,but the relative intensities within both series are correct. The correctness of the curves is testified to by the fact that the pairs of H(A,Ti) and H(t,Ti) curves corresponding to the same temperature cross each other at the Analytical Chemistry, Vol. 67, No. 20, October 15, 1995
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same frequency for all temperatures (at the frequency where the “physical slit width” is the same for both representations). Regarding FT-IR emission spectrometry, it should be pointed out that since FT-IR spectrometers produce spectra at constant resolution in wavenumber, it is the wavelength representation, eq 3, that should be used as theoretical reference blackbody radiation.15 Measurement of Emission: Temperature of the Detector and Instrument Response. If the radiation of a blackbody at absolute temperature Tis detected by an ideal FT-IR spectrometer having 100%throughput, no stray light, and detector with blackbody characteristics kept at 0 K, spectra coincident with a Planck function, H(ij,T), would be obtained. Radiation emitted by a non-blackbody having emittance E@) is described by the function E(+)H(F,T),which can be viewed as the emittance spectrum of the sample modulated by the Planck function. If the detector in not at 0 K, only the radiation balance between the detector and sample (plus surroundings) is measured. Although this principle is stated by Chase5and quoted by DeBlase and C~mpton,’~ the expression they have given for the radiation detected by the spectrometer does not reflect this circumstance:
L(+,T)= R(F)[E,(+)H(F,T)+ B(C)
+ I(F)Q(+)]
(4)
where R(F) is the instrument response function, and El(+) and I(+)@(+) represent stray radiation (background radiation and instrument self-emission reflected off the sample surface, respectively). To be correct, in place of E,(ij)H(+,T),eq 4 should contain the difference of radiation fluxes coming from the sample and from the detector:
where subscripts s and d denote sample and detector, respectively. The above correction, however, has no consequence on the measurement of sample emittance if it is done according to the two-temperature, four-measurement approach.s,zl It gains real significance when single-beam emission spectra are studied using a room temperature detector. In this case, stray radiation originating from room temperature parts of the spectrometer can be neglected, and, if Ed(+) is close to unity (most detectors are good approximations to a blackbody radiator), the measured single-beam spectrum can be described as
When both the sample and the detector are blackbodies (E,@) = Ed(+) = 1) kept at two different temperatures, we arrive at an
even simpler formula,
L,(+,T) = R(F)[H(+,TJ- H(G,Td)l
(7)
corresponds to the use of eq 7. It appears to be an effective way of correcting for detector temperature. From eq 7, it follows that if the sample is at a lower temperature than the detector, L(+,T)will be negative, showing that the net radiation flux is directed from the detector toward the sample. In this case, the interferogram appears inverted (turned upside down), but the single-beam spectrum obtained after Fourier transformation and phase correction will be the same as in the case of positive temperature difference, T, - Td. It is interesting to note that according to eq 6, for a room temperature detector and heated sample having strong discrete emission bands, L(ij,T) can be positive at somefrequencies (at the peaks of the emission bands of the sample) and negative ut others (in transparent regions of the sample spectrum), meaning that radiation of differentfrequencies can travel in opposite directions. We wonder if this possible state of events born out by sheer speculation will ever receive experimental confirmation. Intensity Scales and Quantitative Evaluation. Thermally excited FT-IR emission spectra recorded in the conventional way, with the sample at elevated temperature, are usually presented in one of the following intensity scales: (i) single-beam emission (energy) spectrum; (ii) relative emittance, Le., emission of the sample relative to that of a reference or background material (e.g., the empty heater plate, the untreated sample, etc.); (ii) emittance, E or moo, Le., the single-beam emission spectrum of the sample divided by that of a laboratory blackbody measured at the same temperature, or emittance spectra obtained by the four-measurement, two-temperature approach;jJ1 and (iv) reflection-corrected emittance, E*, Le., same as iii above, but with the use of an optically opaque (very thick) reference of the same material as the sample instead of the blackbody?,10 Of these, presentation i is not really acceptable because its band intensities are modulated by the shape of the Planck blackbody radiation and by the instrument response function, which can mask useful spectral information. Spectral presentation ii eliminates the wavenumber dependence of the instrument response but may produce unpredictably high intensity values, and the noise level may increase enormously in regions of low (near zero) emission of the reference material. Emission spectra obtained using a blackbody reference (as under iii) ensures true relative band intensities, but distortions due to dispersion of surface reflectivity or to self-absorption may still be present. In order to eliminate such distortions from the spectra, the so-called reflection-corrected emittance, E*, was proposed by Hvistendahl et aLg and Rytter.’O This way, true relative band intensities are obtained with no distortions at all. Note, however, that the emittance scale, E, or rather 1 - E, is analogous to transmittance in absorption spectroscopy in the sense that it is not linearly proportional to thickness (d)or concentration (c),and its maximum value, in principle, is 1. In order to convert the emittance spectrum, E @ ) , to a linear intensity scale termed by us emissivity, ~ ( i j ) the , negative logarithm of 1 - E@) has to be taken:
-log,& The correction scheme we proposed in a recent note15to achieve a fair comparison between measured and theoretical blackbody curves (e.g., for the measurement of the sample temperature) (21) Kember, D.; Chenery, D. H.; Sheppard, N.; Fell, J. Spectrochim. Acta 1979, 35A. 445-459.
3784 Analytical Chemistry, Vol. 67, No. 20, October 15, 1995
- E(F)1 = €(+)Cd
(8)
Equation 8 can be called the Lambert-Beer law of emission spectroscopy. If we are concerned only with the internal properties of the sample and exclude surface effects (reflection), 1 E(+) can be replaced by the transmittance of the sample, t(ij),
and we get the customary form of the Lambert-Beer law used in absorption spectrometry,where E @ ) denotes the molar (decadic) absorption coefficient. Thus, if reflection can be neglected, eq 8 defines the decadic absorbance, AIO, and can be used for quantitative determinations. The transformation of emittance spectra to absorbance according to eq 8 is similar to, but unfortunately not quite the same as, conversion of transmittance spectra to absorbance, because the argument of log is 1- E@),which requires an operation (constant array minus spectrum) not readily available in the ET-IR software of many commercial instruments. In the lack of the proper operation (and perhaps because of the similarity of the terms emittance and absorbance), emittance data are often treated like absorbance data, and all kinds of data manipulations allowed for absorbance spectra are performed with emittance spectra. However, it is important to realize that most operations, like spectral subtraction, baseline correction, deconvolution,curve fitting, etc., are “illegal” in the emittance scale because they require a linear intensity scale. Although an expression similar to eq 8 appeared (with a printing error) in an early paper by Grif6ths,4 it has been ignored even in some works dealing with quantitative determinations.22 Equation 8 assumes that the measured emittance spectrum, E@), is connected to the internal property of the sample, emissivity, E (C) , as
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where x = & is the effective thickness (Le., sample thickness times concentration). Note that it is E ( + ) , not E(+),that can be approximated by a sum of Lorentzian/Gaussian functions. It it most unfortunate and may add to the confusion of these two quantities that the accepted IUPAC nomenclaturez3uses the same symbol, 6,for both emittance (E in this paper) and molar decadic absorption coefficient, quantities appearing simultaneouslyin both eqs 8 and 9. Spectral Distortions Due to Self-Absorptionor Improper Data Manipulations. In view of the previous discussion, eq 9 can be written in short as
E(+) = 1 - t(9) where t(C) is the transmittance of the sample. Rytterlo has shown (using a different notation) that the effect of reabsorption of bulk emission by a cooler surface layer manifested in splitting or inversion of the centers of strong emission bands can be modeled by the expression E(9) = (1 - t&,
where tb and ts are transmittances of the bulk and of the surface layer, respectively. In fact, a simpler expression, (22) Tilotta, D. C.; Busch, M. A; Busch, K W. Appl. Spectrosc. 1991,45, 178185. (23) Mills, I.; CVitas, T.; Homann, IC; Kallay, N.; Kuchitsu, K. Quantities, Units and Symbols in Physical Chemistry, IUPAC, 2nd ed.; Blackwell ScientSc Publications: Oxford, 1993; pp 31-32.
Figure 2. Simulation of the effect of self-absorption using eq 12 for different effective thicknesses of emitting bulk (xb) and absorbing surface layer (xs). (Lorentzianband shapes with 50 = 600, lo = 2000, and w = 30 cm-l.)
E(?) = (1 - t d t , referring to a single pass of the emitted radiation through the sample (i.e., no reflecting back plate) can describe the effect of self-absorptionand simulate the inversion or splitting of emission bands just as well. The successful simulation shown on the examples of Figure 2 proves that this effectof selfabsorption is due to the interplay of nonlinearity of both emittance and transmittance scales and their opposite directions. Furthermore, it can be readily shown that illegal spectral manipulations such as subtraction done in a nonlinear intensity scale (e.g., emittance or all those listed under i-iv) can lead to distortions that can be mistaken for the effect of surface reflectivity or reabsorption. The only way to avoid the spectral artifacts of illegal data manipulation is to transform the emittance spectra in accordance with eq 8 to a linear intensity scale, emissivity, before spectral manipulations. The incorporation of the corresponding operation (Le., a constant minus doublebeam spectrum) into ET-R emission spectroscopy software packages is strongly recommended to instrument manufacturers. Emission-Absorption SpectnwcoWof Multhyer Samples. The starting point of our discussion here is the assumption that self-absorption is a common phenomenon occurring most of the time when the sample is heated from the rear side so that the cooler surface layer can absorb radiation emitted by the inner parts or deeper-lying layers. Analytical Chemistry, Vol. 67,No. 20,October 15, 1995
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Wavenumberr Figum 3. Emission Spectrum of a 6 r m Mylar sheet on a heated shiny metal plate (lower trace). and emission-absorption spenrum of the same Mylar meet on a heated meta plate covered with mane blaw pamt (upper trace)
Figure 4. Notation of layers in a two-layer sample depending on the temperature gradient within the sample in an emission-absorption experiment. (A) The cool absorbing surface layer is thicker than layer 2 (d &). ( 6 ) The absorbing layer is thinner than layer 2 (d. < 6).
'This assumption has been verified by two simple measurements, the results of which are shown in Figure 3. In the 6rst case Figure 3, lower trace), a 6 pm thick Mylar sheet was attached to the sample holder (a heated, polished metal plate), while in the second case Figure 3, upper trace), the Mylar sheet was attached to a laboratory blackbody (a similar metal plate covered with matte black paint). Both spectra were measured at the same temperature and ratioed against the same singlebeam blackbody emission spectrum. The resulting spectra show clearly that while the lower spectral trace in Figure 3 is a usual emittance spectrum (with signs of self-absorption near the peaks of the strongest bands), the other one can be regarded as the absorption (transmittance) spectrum of the Mylar sheet, or more correctly, as an emission-ubsorption spectmm where the deeper-lying layer of the sample (the black paint) is emitting while the upper layer of the sample (the Mylar sheet) is absorbing radiation. It is quite natural that when a homogeneous or singk-fuyer sample is studied by IR emission, the distorting effect of self3786 Analytical Chemistiy, Vol. 67, No. 20, October 15, 1995
absorption can occnr only at the center of (strong) emission bands. In multikzyersamples, however, when the emitting bulk and the absorbing surface layer are structurally or even chemically different, the emission and absorption bands may be at very different frequencies, the combination of which produces a complicated picture: this is a singlebeam absorption spectrum in which the source radiation may be far from continuous. 'The observed spectrum of such samples will depend on the thicknesses of the different layers (d,, dz, etc.) within the composite sample on the one hand, and on the distribution of temperature, i.e., on the thicknesses of emitting (de) and absorbing portions on the other. Absorption-emission spectra (AEs) of multilayer samples can be simulated using a mathematical approach similar to eq 12, taking into account that layers that are chemically (structurally)
(a,
E = 11- 1 0 - ~ i ( ~ ) ) d c i - r z ( ~ ) ) d c z l
(13)
On varying the thicknesses of emitting and absorbing layers, this equation can lead to very different results. Naturally, the conditions of the IR emission experiment can be varied as well, applying different cooling and heating regimes as in TIRES1J2or TIKlXZ4 As an example, the simulation of IR emission spectra of mixed IrOz/TiOz electrocatalytic layers on a Ti plate is shown in Figure 5. The "theoretical" spectrum closest to the measured one (see Figure 6 of ref 25) is that in Figure 5C, which was obtained on the assumptions that a 5 pm Ti02 layer is formed on top of a 10 pm 11-02 layer and that the upper layer is only absorbing the radiation emitted by the lower layer. In principle, if the absorption spectra of the pure components (layers) making up the sample are known, a kind of depth profiling can be carried out by varying the heating-cooling equilibrium in the sample, accompanied by simulations of emission-absorption spectra. These capabilities of IRES are not explored yet completely. Although it is not expected that this method can compete with the depth profiling potential of the photoacoustic (PA) technique, it may be handy when PA cannot be used, e.g., under conditionsof remote sensing or in on line or in situ measurements. Further refinement of the procedure is envisaged by taking into account also the population of the vibrational energy levels, depending on the temperature of the layers.
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WAVENUMBER Figure 5. Simulation of the IR emission-absorption spectrum of an electrocatalytic lr02/ri02 film having a layered structure. The hypothetical absorption spectra of layers 1 and 2 (lower two traces) were chosen to produce an emission-absorption spectrum (upper trace) closely resembling the measured emission spectrum (see Figure 6 of ref 25).
different have different spectral distributions (see F i r e 4 for notations used in the case of two layers):
ACKNOWLEDGMENT Financial support from the Hungarian National ScienMc Research Fund, OTKA (Grant No. 1892), and COST (Project D5, ERBCIPECT 92-6104) is gratefully acknowledged. The authors thank the referees for useful suggestions to improve the presentation of this work. Received for review February 28, 1995. Accepted July 16, 1995.a
AC9502110 e. Abstract published in Advance ACS Abstracts, September 1, 1995.
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