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Linewidth of the ESR modulation spectrum
Volume 175, number 5
CHEMICAL PHYSICS LETTERS
21 December 1990
Linewidthof the ESR modulationspectrum I. Miyagawa, G. Iyer and F.B. Majid Department of Physics and Astronomy, The Univewty ofAlabama, Tuscaloosa, AL 35487-0324, GSA Received 17 September I990
In the case of an X-ray irradiated fused quartz, the ESR modulation spectral line at 77 K was found to consist of two components instead of the reported single component. The linewidth of the broad component was shown to be characterized by T, of the individual spin packet in accordance with the partial-saturation theory of DulEiC and PeriC, and that of the sharp component by T, in accordance with the three-photon theory of Giordano et al.
1. Introduction
2. Experimental
Several groups [ l-51 have observed sharp spectral lines from inhomogeneously broadened electron-spin resonance (ESR) lines under multiple modulation when one of the modulation frequencies is swept. Giordano et al. [ 31 have proposed that this modulation spectrum (MS) originates from a nonlinear effect or a three-microwave-photon process. This three-photon theory suggests that the linewidth of MS is given by 2/T,, T, being the longitudinal relaxation time. Belov and Milov [ 51, who will be referred to as BM, have observed MS, electron-spin echo, and pulse signals from an irradiated fused quartz, and obtained a result favorable to the threephoton theory. Then, DulEiC and PeriC [ 61 have reported a theory based on the Bloch equation, and proposed that MS originates from a partial microwave saturation involving many sideband fields. This partial-saturation theory suggests that the linewidth is given by 2/T, of the individual spin packet, T, being the transverse relaxation time, in contrast to the suggestion of the three-photon theory and the experimental conclusion of BM. The partial-saturation theory appeared shortly after the paper by BM was published, who apparently did not have an opportunity to examine this theory before their reporting. For this reason, we conducted a study of MS from a sample similar to that used by BM, carefully examining the signal under a low-microwave-power range.
The MS signals were observed with the spectrometer reported in ref. [ 11. The sample was a fused quartz (Wilmad Glass Company 707 SQ) irradiated in an X-ray source operating at 45 kV and 30 m.4 at a rate of approximately 5 X 1O4R/min at room temperature. Most of the observations were made with a specimen irradiated for 10 min under the first modulation of frequency (wJ2n) 20 kHz and amplitude (&) 1.4 G and the second modulation for sweep (&&/2x) of amplitude (&) 0.22 G, unless otherwise described.
3. Results and discussion 3.1.
MS measurements
Figs. 1 and 2 show the MS signals at 298 and 77 K, respectively, as a function of microwave power. The signals are much more sensitive to power at 77 K than at 296 K. In particular, the signal at 77 K under low powers consists of two components in contrast to the single line reported by BM. The sharp component ( 1) is sensitive to power while the broad component is much less sensitive than the signal at 298 K. A much better separation of the two components was accomplished under some conditions, although the lines were substantially broader (see fig. 2b).
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
441
125 kHz
115 L_+-20
dB
-23
-26
dB
dB
Fig. 1. MS signals at 298 K as a function of relative microwave power. 125 kHz
115 (al
2 I December 1990
CHEMICAL PHYSICS LETTERS
Volume 175, number 5
-20
TV-
dB
where n=O, I I, 22, . and n’= &l, &2, . . . The primary lines for which the linewidth is defined are given by n’ = YL1, and the linewidth for a secondary line is inversely proportional to 1n’I. Since, in general, the observed line for 1n’I= 1 is not a pure primary one but rather an overlap of many lines different in n’, the apparent linewidth is expected to be substantially sharper than the true linewidth. Fortunately, however, the contribution of the secondary lines decreases drastically with decreasing HE,. Consequently, one can obtain an accurate linewidth by measuring the apparent linewidth as a function of Hf, and by confirming it to be independent of HE, in the low Hf, range. In addition, the observed line is substantially broadened under high microwave powers, as was shown in the case of component ( 1) at 77 K. Thus, the apparent linewidth needs to be observed as a function of microwave power, and the value obtained by extrapolation to zero power should be used for the procedure described above, as is shown in fig. 3 for the case of the signal at 298 IL From the solid curve, the half-height linewidth A1,2 was estimated to be 1.2 kKz, or 3.8~ 103/s which is the corresponding reciprocal relaxation time ( 1/r) given by ~A,,z (see ref. [ 51). Table 1 lists the estimated values of l/7 for the signal at 298 K and for the two components at 77 K,
T-23 dB -29
dB
Fig. 2. MS signals at 77 K. (a) Curves similar to those in fig. 1; (b) curveforw,/2x=50
kHz. H,=O.7
G, andH&=O.OJG.
No evidence for such signal separation was obtained at 298 K even for low microwave powers (see fig. 1). 3.2. Estimation of the linewidth
I
It has been shown [ 1 ] that the spectral lines of MS appear at w’, = -n(wJn’
442
),
(1)
0.00 0.00
0.20
0.40
0.60
0
30
H&G) Fig. 3. Apparent linewidth of the signal at 298 K versus Hb for the low-microwave-power limit. The dotted curve was obtained for - 20 dB.
Volume 175, number 5
CHEMICAL PHYSICS LETTERS
Table I Reciprocal relaxation times ( 1/r) corresponding widths and 1/‘f, and 1/T2 in units of IO-‘/s Component
298 K 71 K
(1)
(2)
3.8& 1.0 0.09 f 0.02
3.8kl.O
IIT,
4.5 4.5
4.9 0.24
December1990
2.0 ,
to the line-
IIT,
21
which were obtained in the manner described above. The values of 1/T, and 1/T2, which are also listed in the same table, are those reported by BM.
0.0
1
3.3. Natwe of the MS lines -2.75 In table 1, one finds that l/7 of component (2) and l/ T2 at 77 K are identical within experimental error. Thus, it was concluded that the linewidth of component (2) is given by 2/T,, suggesting that component (2) was detected through the partial-saturation process. Moreover, one finds that at 77 K, l/r of component ( 1) agrees fairly well with 1/T,. Although the agreement is not complete, it was concluded that the linewidth of component ( 1) is given by 2/T,? suggesting that this signal was detected through the threephoton process, for the reason to be given below. In a three-photon process in general, the signal intensity is known to be proportional to P3, where P is the relative microwave power [ 31. Since the linewidth depends on P substantially, the integrated intensity of component (l), N,, was calculated, and log N, was plotted against log P, as shown in fig. 4. From this plot, the slope of the straight line was estimated to be 3.1, supporting the three-photon theory which predicts the detected linewidth to be 2/Ti. A similar calculation was made for component (2), and the slope was estimated to be 2.1 (see the plot for PJZ in fig. 4). This slope value supports the partial-saturation process, since in the expansion of the ESR intensity in a series of P, the lowest term representing the saturation effect is proportional to P’. The value of l/r at 298 K, where no signal separation was observed, agrees with both l/T, and 1/ T2 within experimental error (see table 1). The signal intensity at this temperature is known to be proportional to P3 [ 31. In the present study, the same
-1.75
-0.75
0.25
log P Fig. 4. Log AI versus log P.
Here,Al is the relativeintegrated
intensity.
proportionality was obtained for the integrated intensity except for the high-microwave-power range. Thus, when T, z T,, the three-photon process was dominant in detection of the MS signal. In conclusion, both Ti and T, of the individual spin packet can be measured with the use of the MS technique, according to the present study. This conclusion is in contrast to that of other authors [ 3,5,6], that is, that only T, or T2 can be measured. When T, >> T,, T, is obtained through the three-photon process, and T2 through the partial-saturation process. When Tl P T,, the three-photon process is much more sensitive to the relaxation than the partial saturation process. 3.4. Remarks The linewidths of the observed MS were found to increase with increasing radiation dose significantly but only slightly. For example, the linewidth for a sample irradiated for 60 min was broader than that for 10 min by 30%, the difference being comparable to experimental error. According to a previous study on irradiated samples of fused quartz [4], several other lines with large linewidths should be detected in addition to the line studied in the present project. 443
Volume 175,number 5
The linewidths
of these lines
CHEMICALPHYSICSLETTERS
are still under
investigation.
References [ I] B. Rakvin, T. Islam and 1. Miyagawa,Phys. Rev. Letters 50 (1983) 1313.
444
21 December 1990
[21 B. Rakvin, Chem. Phys. Letters 109 ( 1984) 280. [ 31 B. Giordano, M. Martinelli, L. Pardi, S. Santucci and C. Umeton, Phys. Rev. A 34 (1986) 264. [4] J.T. Swann Jr. and I. Miyagawa,J. Chem. Phys. 86 (1987) 1157. [ 51P.G. Belowand A.D. Milov,Chem. Phys. Letters 15I ( 1988) 79. [61 A. Dul% and M. PeriC,J. Magn. Reson. 76 (1988) 427.
CHEMICAL PHYSICS LETTERS
21 December 1990
Linewidthof the ESR modulationspectrum I. Miyagawa, G. Iyer and F.B. Majid Department of Physics and Astronomy, The Univewty ofAlabama, Tuscaloosa, AL 35487-0324, GSA Received 17 September I990
In the case of an X-ray irradiated fused quartz, the ESR modulation spectral line at 77 K was found to consist of two components instead of the reported single component. The linewidth of the broad component was shown to be characterized by T, of the individual spin packet in accordance with the partial-saturation theory of DulEiC and PeriC, and that of the sharp component by T, in accordance with the three-photon theory of Giordano et al.
1. Introduction
2. Experimental
Several groups [ l-51 have observed sharp spectral lines from inhomogeneously broadened electron-spin resonance (ESR) lines under multiple modulation when one of the modulation frequencies is swept. Giordano et al. [ 31 have proposed that this modulation spectrum (MS) originates from a nonlinear effect or a three-microwave-photon process. This three-photon theory suggests that the linewidth of MS is given by 2/T,, T, being the longitudinal relaxation time. Belov and Milov [ 51, who will be referred to as BM, have observed MS, electron-spin echo, and pulse signals from an irradiated fused quartz, and obtained a result favorable to the threephoton theory. Then, DulEiC and PeriC [ 61 have reported a theory based on the Bloch equation, and proposed that MS originates from a partial microwave saturation involving many sideband fields. This partial-saturation theory suggests that the linewidth is given by 2/T, of the individual spin packet, T, being the transverse relaxation time, in contrast to the suggestion of the three-photon theory and the experimental conclusion of BM. The partial-saturation theory appeared shortly after the paper by BM was published, who apparently did not have an opportunity to examine this theory before their reporting. For this reason, we conducted a study of MS from a sample similar to that used by BM, carefully examining the signal under a low-microwave-power range.
The MS signals were observed with the spectrometer reported in ref. [ 11. The sample was a fused quartz (Wilmad Glass Company 707 SQ) irradiated in an X-ray source operating at 45 kV and 30 m.4 at a rate of approximately 5 X 1O4R/min at room temperature. Most of the observations were made with a specimen irradiated for 10 min under the first modulation of frequency (wJ2n) 20 kHz and amplitude (&) 1.4 G and the second modulation for sweep (&&/2x) of amplitude (&) 0.22 G, unless otherwise described.
3. Results and discussion 3.1.
MS measurements
Figs. 1 and 2 show the MS signals at 298 and 77 K, respectively, as a function of microwave power. The signals are much more sensitive to power at 77 K than at 296 K. In particular, the signal at 77 K under low powers consists of two components in contrast to the single line reported by BM. The sharp component ( 1) is sensitive to power while the broad component is much less sensitive than the signal at 298 K. A much better separation of the two components was accomplished under some conditions, although the lines were substantially broader (see fig. 2b).
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)
441
125 kHz
115 L_+-20
dB
-23
-26
dB
dB
Fig. 1. MS signals at 298 K as a function of relative microwave power. 125 kHz
115 (al
2 I December 1990
CHEMICAL PHYSICS LETTERS
Volume 175, number 5
-20
TV-
dB
where n=O, I I, 22, . and n’= &l, &2, . . . The primary lines for which the linewidth is defined are given by n’ = YL1, and the linewidth for a secondary line is inversely proportional to 1n’I. Since, in general, the observed line for 1n’I= 1 is not a pure primary one but rather an overlap of many lines different in n’, the apparent linewidth is expected to be substantially sharper than the true linewidth. Fortunately, however, the contribution of the secondary lines decreases drastically with decreasing HE,. Consequently, one can obtain an accurate linewidth by measuring the apparent linewidth as a function of Hf, and by confirming it to be independent of HE, in the low Hf, range. In addition, the observed line is substantially broadened under high microwave powers, as was shown in the case of component ( 1) at 77 K. Thus, the apparent linewidth needs to be observed as a function of microwave power, and the value obtained by extrapolation to zero power should be used for the procedure described above, as is shown in fig. 3 for the case of the signal at 298 IL From the solid curve, the half-height linewidth A1,2 was estimated to be 1.2 kKz, or 3.8~ 103/s which is the corresponding reciprocal relaxation time ( 1/r) given by ~A,,z (see ref. [ 51). Table 1 lists the estimated values of l/7 for the signal at 298 K and for the two components at 77 K,
T-23 dB -29
dB
Fig. 2. MS signals at 77 K. (a) Curves similar to those in fig. 1; (b) curveforw,/2x=50
kHz. H,=O.7
G, andH&=O.OJG.
No evidence for such signal separation was obtained at 298 K even for low microwave powers (see fig. 1). 3.2. Estimation of the linewidth
I
It has been shown [ 1 ] that the spectral lines of MS appear at w’, = -n(wJn’
442
),
(1)
0.00 0.00
0.20
0.40
0.60
0
30
H&G) Fig. 3. Apparent linewidth of the signal at 298 K versus Hb for the low-microwave-power limit. The dotted curve was obtained for - 20 dB.
Volume 175, number 5
CHEMICAL PHYSICS LETTERS
Table I Reciprocal relaxation times ( 1/r) corresponding widths and 1/‘f, and 1/T2 in units of IO-‘/s Component
298 K 71 K
(1)
(2)
3.8& 1.0 0.09 f 0.02
3.8kl.O
IIT,
4.5 4.5
4.9 0.24
December1990
2.0 ,
to the line-
IIT,
21
which were obtained in the manner described above. The values of 1/T, and 1/T2, which are also listed in the same table, are those reported by BM.
0.0
1
3.3. Natwe of the MS lines -2.75 In table 1, one finds that l/7 of component (2) and l/ T2 at 77 K are identical within experimental error. Thus, it was concluded that the linewidth of component (2) is given by 2/T,, suggesting that component (2) was detected through the partial-saturation process. Moreover, one finds that at 77 K, l/r of component ( 1) agrees fairly well with 1/T,. Although the agreement is not complete, it was concluded that the linewidth of component ( 1) is given by 2/T,? suggesting that this signal was detected through the threephoton process, for the reason to be given below. In a three-photon process in general, the signal intensity is known to be proportional to P3, where P is the relative microwave power [ 31. Since the linewidth depends on P substantially, the integrated intensity of component (l), N,, was calculated, and log N, was plotted against log P, as shown in fig. 4. From this plot, the slope of the straight line was estimated to be 3.1, supporting the three-photon theory which predicts the detected linewidth to be 2/Ti. A similar calculation was made for component (2), and the slope was estimated to be 2.1 (see the plot for PJZ in fig. 4). This slope value supports the partial-saturation process, since in the expansion of the ESR intensity in a series of P, the lowest term representing the saturation effect is proportional to P’. The value of l/r at 298 K, where no signal separation was observed, agrees with both l/T, and 1/ T2 within experimental error (see table 1). The signal intensity at this temperature is known to be proportional to P3 [ 31. In the present study, the same
-1.75
-0.75
0.25
log P Fig. 4. Log AI versus log P.
Here,Al is the relativeintegrated
intensity.
proportionality was obtained for the integrated intensity except for the high-microwave-power range. Thus, when T, z T,, the three-photon process was dominant in detection of the MS signal. In conclusion, both Ti and T, of the individual spin packet can be measured with the use of the MS technique, according to the present study. This conclusion is in contrast to that of other authors [ 3,5,6], that is, that only T, or T2 can be measured. When T, >> T,, T, is obtained through the three-photon process, and T2 through the partial-saturation process. When Tl P T,, the three-photon process is much more sensitive to the relaxation than the partial saturation process. 3.4. Remarks The linewidths of the observed MS were found to increase with increasing radiation dose significantly but only slightly. For example, the linewidth for a sample irradiated for 60 min was broader than that for 10 min by 30%, the difference being comparable to experimental error. According to a previous study on irradiated samples of fused quartz [4], several other lines with large linewidths should be detected in addition to the line studied in the present project. 443
Volume 175,number 5
The linewidths
of these lines
CHEMICALPHYSICSLETTERS
are still under
investigation.
References [ I] B. Rakvin, T. Islam and 1. Miyagawa,Phys. Rev. Letters 50 (1983) 1313.
444
21 December 1990
[21 B. Rakvin, Chem. Phys. Letters 109 ( 1984) 280. [ 31 B. Giordano, M. Martinelli, L. Pardi, S. Santucci and C. Umeton, Phys. Rev. A 34 (1986) 264. [4] J.T. Swann Jr. and I. Miyagawa,J. Chem. Phys. 86 (1987) 1157. [ 51P.G. Belowand A.D. Milov,Chem. Phys. Letters 15I ( 1988) 79. [61 A. Dul% and M. PeriC,J. Magn. Reson. 76 (1988) 427.