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Luminescence spectra at bending fracture of single crystal MgO
PERGAMON
Solid State Communications 117 (2001) 17±20
www.elsevier.com/locate/ssc
Luminescence spectra at bending fracture of single crystal MgO Y. Kawaguchi Chugoku National Industrial Research Institute, Kure, Hiroshima 737-0197, Japan Received 1 September 2000; accepted 3 October 2000 by S. Ushioda
Abstract Luminescence at bending fracture of single crystal MgO is investigated. Emission bands at about 400±500 and 730 nm are observed in the fractoluminescence spectra. The former emission decays within several microseconds while the latter decays in several hundreds of microseconds. By comparing with the result of photoluminescence, the 400±500 nm band in the fractoluminescence should be assigned to an intrinsic defect center, while the 730 nm band is due to Cr 31 impurity. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: C. Point defects; D. Optical properties; E. Luminescence PACS: 78.60.M; 61.72
Accompanying mechanical deformation and fracture of a material, emission of energetic electrons, ions, neutral particles and photons is observed. This phenomenon is called fractoemission [1±3], and fractoluminescence for photon emission [4±8]. Fractoemission can be a useful tool for investigating dynamic processes on the fracture surface of a material. It is also related with electromagnetic anomalies before large earthquakes, so-called seismic electromagnetic signal (SES) [9±13]. In this paper, fractoluminescence in single crystal MgO has been investigated and the origin of the luminescence is discussed. MgO is a typical wide bandgap insulator, and the electronic and optical properties have been investigated in detail [14±22], and several works on fractoemission of MgO have been also reported [1±4]. A single crystal MgO (99.9% purity) from Ohyo±Koken Co. was cleaved to a rectangle of 10 £ 15 £ 2 mm 3 along the k100l plane, and set to a small three-point bending apparatus assembled to a vacuum chamber. Impurity contents of the sample are shown in Table 1. The pressure was kept to 1.3 £ 10 25 Pa. The load applicator of the bending apparatus was proceeded at 2 mm/min, and time response of positive charge emission, negative charge emission, applied load, and luminescence was measured simultaneously. The gate time of photon counter for luminescence measurement was set to 10 ms. For the measurement of luminescence spectra, emitted light was focused on the entrance slit of the spectrometer and measured with an optical multichannel
analyzer. Time-resolved photoluminescence (PL) spectra from MgO crystal were measured and compared with fractoluminescence spectra. 5 eV photons of KrF excimer laser (MPB Technology PSX-100) were irradiated to the sample, and PL was measured with the optical multichannel analyzer attached to the spectrometer. The ratio of the gate width to the delay time was ®xed to 1/5. Details of the experimental setup are described elsewhere [6±8]. Fig. 1 shows time response of fractoemission at bending fracture of single crystal MgO at 1.3 £ 10 25 Pa. Negative charge emission, positive charge emission, and luminescence start at the instant of bending fracture of the sample. Large emission of negative charge lasts about 10 ms after fracture, and small emission continues several hundreds of milliseconds. Bursts of positive charge emission are observed intermittently within several tens of milliseconds after fracture. While, luminescence peaks at fracture, and decays within several milliseconds. Time-response of fractoluminescence in MgO is shown semi-logarithmically in Fig. 2. The solid line is a result of curve ®tting with a sum of two exponential decay functions, I t
2 X i1
Ai £ exp2t=ti :
1
The decay times are about several microseconds and several hundreds of microseconds, respectively. It should be remarked that the decay time of the fast component is just
0038-1098/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00413-0
18
Y. Kawaguchi / Solid State Communications 117 (2001) 17±20
Table 1 Impurity contents in MgO samples (in wt. ppm) Na and K
Ca
Al
Fe
Si
S
Cl
F
Cr
V
Mn
Ni
Ti
Zn
B
P
C
5
40
15
50
10
5
7
3
10
3
4
3
2
1
5
2
10
the same order with the time resolution in the present experiment. Fig. 3 shows fractoluminescence spectra of MgO. Because of the wide slit width for maximum ef®ciency of detecting light, the bandwidth of the measurement system is as large as 20 nm. A very large emission band centered at about 730 nm is observed. Another emission band is situated around 400±500 nm, though very weak and the central wavelength is not clear. Fig. 4 shows time response of fractoluminescence with and without an optical ®lter transmitting light of only l . 560 nm. The fast decaying component is terribly weakened with the optical ®lter. Thus, the wavelength of the fast decaying emission must be shorter than 560 nm, and the wavelength of the slow decaying emission is longer than 560 nm. This result shows that the 400±500 nm band in the fractoluminescence spectra is the fast decaying emission, and that the 730 nm band is the slow decaying emission. Fig. 5 shows PL spectra in MgO under irradiation of KrF
Fig. 1. Time response of fractoemission at bending fracture of MgO in a vacuum: (a) negative charge; (b) positive charge; (c) luminescence; (d) load.
Fig. 2. Time-response of fractoluminescence in MgO with a semilogarithmic scale: dots-experimental data; solid line-result of curve ®tting.
excimer laser, and time-resolved PL spectra are shown in Fig. 6. Initially, the 500 nm band is seen within 1 ms of the delay, and then the 430 nm band appears around 5±10 ms of the delay. Another band around 730±750 nm grows from 5±10 ms of the delay, and is accompanied by a ®ne structure around 1 ms of the delay. This ®ne structure is just due to Cr 31 impurity as discussed below [16]. Four models are proposed for the mechanism of fractoluminescence [6,11]: (i) relaxation luminescence of excited ions emitted from the fracture surface; (ii) discharge of the ambient gas; (iii) blackbody radiation due to local heating of
Fig. 3. Fractoluminescence spectra in MgO: (a) VIS region; (b) VIS±IR region.
Y. Kawaguchi / Solid State Communications 117 (2000) 17±20
19
Fig. 4. Time-response of fractoluminescence in MgO: solid linewithout an optical ®lter; dotted line-with an optical ®lter cutting light of l , 560 nm.
the fracture surface; (iv) relaxation luminescence of defect centers created and excited by mechanical fracture. As shown in Fig. 1, time response of luminescence upon bending fracture of MgO is much different from that of positive and negative charge emission. Thus, the ®rst possibility is not accepted. Moreover, the possibility of gas discharge is denied because our experiment is done in high vacuum, 10 25 Pa. The possibility of blackbody radiation is also denied because the spectrum of blackbody radiation with similar peak wavelength is several times broader than that of fractoluminescence and the spectral shape is totally different. The remaining model, relaxation luminescence of defect centers, is reasonable because progress of crack causes bond-breaking and nuclear motion, and promotes release of atoms and ions from the lattice sites, resulting in the creation of defects. Moreover, the movement of the dislocation mechanically excites defects [5].
Fig. 5. PL spectra in MgO by KrF irradiation: (a) VIS region; (b) VIS±IR region.
Fig. 6. Time-resolved PL spectra in MgO by KrF irradiation.
To clarify the defects causing the fractoluminescence, we compared the luminescence with PL. As mentioned in the previous section, fractoluminescence spectrum shows two bands: 400±500 nm and 730 nm. Decay time of the former band is several microseconds or smaller, while that of the latter band is several hundred microseconds. While, PL spectrum consists of mainly three bands: 500 nm band which peaks within 1 ms, 430 nm band which peaks around 5±10 ms, and 730 nm band which peaks around several hundreds of microsecond. Peak position and the order of the decay time of the 730 nm band in PL agree well with those in fractoluminescence, so that the origin of that band must be the same. Fine structure on the 730 nm band is not observed in fractoluminescence spectrum because of the wide slit width and low resolution of the wavelength on the fractoluminescence measurement. Chao [16] reported a red band which peaks at about 700 nm with vibrational sidebands lines in thermoluminescence spectrum of MgO, and assigned the band to Cr 31 impurity. On the PL spectra which we observed, the 730 nm band also shows vibrational sidebands though the structure is not so clear due to the lack of the spectral resolution in our spectrometer. Because of the similarity of the peak position and the structure, the 730 nm band in the PL of MgO in our study should be also due to Cr 31 impurity center. Thus, the 730 nm band in the fractoluminescence of MgO is also assigned to the relaxation luminescence of Cr 31 impurity excited by mechanical stress during fracture and crack propagation. As for the 400±500 nm band in fractoluminescence of MgO, the peak position is not clearly speci®ed because of
20
Y. Kawaguchi / Solid State Communications 117 (2001) 17±20
the very small intensity, but the decay time of the band is several microseconds or smaller. In PL, the 500 nm band peaks within 1 ms while the 430 nm band peaks around 5±10 ms. The time response of these two band in PL agrees well within the experimental accuracy with the 400±500 nm band in fractoluminescence, suggesting that the origin of the two are the same. In PL, Rosenblatt and his coworkers [21] reported the 390 and 530 nm bands in time-resolved spectra of MgO with different defect densities, and attributed the bands to F 1 and F center, respectively. The peak positions of the two bands were shifted to several tens of nm depending on the densities of defects, and the 500 nm band peaks within 1 ms while the 390 nm band peaks around 1 ms, depending on the sample conditions. Considering the ambiguity due to the difference of the sample, the two bands on Rosenblatt's work resemble the 430 and 500 nm bands in PL spectra in our study. Thus, the origins of the two bands in PL in our study can be also attributed to F 1 and F centers, and the 400±500 nm band in fractoluminescence may be also assigned to the same defect centers. Upon fracture, ejection of oxygen atoms and ions and creation of oxygen vacancies are expected, and electrons released during fracture will be trapped to the oxygen vacancies resulting in the creation of excited F-type centers. These F-type centers should cause the 400±500 nm emission in fractoluminescence. In summary, luminescence spectra upon bending fracture of MgO crystal in vacuum are investigated. 1. Two emission bands are observed: a large band at about 730 nm; and a weak one around 400±500 nm. 2. The peak position and time response of two fractoluminescence bands are similar to those of PL bands in MgO. 3. The 730 nm band is assigned to be due to Cr 31 impurity, while the 400±500 nm band may be assigned to F-type centers.
References [1] J.T. Dickinson, L.C. Jensen, M.R. McKay, J. Vac. Sci. Technol. A 4 (1986) 1648. [2] J.T. Dickinson, L.C. Jensen, M.R. McKay, J. Vac. Sci. Technol. A 5 (1987) 1162. [3] S.C. Langford, J.T. Dickinson, L.C. Jensen, J. Appl. Phys. 62 (1987) 1437. [4] G.P. Williams Jr., T.J. Turner, Solid State Commun. 29 (1979) 201. [5] T. Hagihara, Y. Hayashiuchi, Y. Kojima, Y. Yamamoto, S. Ohwaki, T. Okada, Phys. Lett. A 137 (1989) 213. [6] Y. Kawaguchi, Phys. Rev. B 52 (1995) 9224. [7] Y. Kawaguchi, Phys. Rev. B 56 (1996) 9721. [8] Y. Kawaguchi, Jpn. J. Appl. Phys. 37 (1998) 1892. [9] P. Varotsos, K. Alexopoulos, Techtonophysics 110 (1984) 99. [10] Y. Enomoto, H. Hashimoto, Electromagnetic Phenomena Related to Earthquake Prediction, Terra Science Publishing Company, Tokyo, 1994, p. 261. [11] Y. Enomoto, H. Hashimoto, Nature 346 (1990) 641. [12] Y. Kawaguchi, Proc. 12th Inter. Symp. Exoemission and its Applications, Polanica, 1997, p. 221. [13] Y. Kawaguchi, Jpn. J. Appl. Phys. 37 (1998) 3495. [14] W.A. Sibley, J.L. Kolopus, W.C. Mallard, Phys. Status Solidi 31 (1969) 223. [15] L.A. Kappers, R.L. Kroes, E.B. Hensley, Phys. Rev. B 10 (1970) 4151. [16] C.-C. Chao, J. Phys. Chem. Solids 32 (1971) 2517. [17] R.D. Newton, W.A. Sibley, Phys. Status Solidi A 41 (1977) 569. [18] R.T. Williams, J.W. Williams, T.J. Turner, K.H. Lee, Phys. Rev. B 20 (1979) 1687. [19] G.P. Summers, T.M. Wilson, B.T. Jeffries, H.T. Tohver, Y. Chen, M.M. Abraham, Phys. Rev. B 27 (1983) 1283. [20] I. Fernandez, J. Llopis, Phys. Status Solidi A 108 (1988) K163. [21] G.H. Rosenblatt, M.W. Rowe, G.P. Williams Jr., R.T. Williams, Y. Chen, Phys. Rev. B 39 (1989) 10309. [22] J.L. Grant, R. Cooper, P. Zeglinski, J.F. Boas, J. Chem. Phys. 90 (1989) 807.
Solid State Communications 117 (2001) 17±20
www.elsevier.com/locate/ssc
Luminescence spectra at bending fracture of single crystal MgO Y. Kawaguchi Chugoku National Industrial Research Institute, Kure, Hiroshima 737-0197, Japan Received 1 September 2000; accepted 3 October 2000 by S. Ushioda
Abstract Luminescence at bending fracture of single crystal MgO is investigated. Emission bands at about 400±500 and 730 nm are observed in the fractoluminescence spectra. The former emission decays within several microseconds while the latter decays in several hundreds of microseconds. By comparing with the result of photoluminescence, the 400±500 nm band in the fractoluminescence should be assigned to an intrinsic defect center, while the 730 nm band is due to Cr 31 impurity. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: C. Point defects; D. Optical properties; E. Luminescence PACS: 78.60.M; 61.72
Accompanying mechanical deformation and fracture of a material, emission of energetic electrons, ions, neutral particles and photons is observed. This phenomenon is called fractoemission [1±3], and fractoluminescence for photon emission [4±8]. Fractoemission can be a useful tool for investigating dynamic processes on the fracture surface of a material. It is also related with electromagnetic anomalies before large earthquakes, so-called seismic electromagnetic signal (SES) [9±13]. In this paper, fractoluminescence in single crystal MgO has been investigated and the origin of the luminescence is discussed. MgO is a typical wide bandgap insulator, and the electronic and optical properties have been investigated in detail [14±22], and several works on fractoemission of MgO have been also reported [1±4]. A single crystal MgO (99.9% purity) from Ohyo±Koken Co. was cleaved to a rectangle of 10 £ 15 £ 2 mm 3 along the k100l plane, and set to a small three-point bending apparatus assembled to a vacuum chamber. Impurity contents of the sample are shown in Table 1. The pressure was kept to 1.3 £ 10 25 Pa. The load applicator of the bending apparatus was proceeded at 2 mm/min, and time response of positive charge emission, negative charge emission, applied load, and luminescence was measured simultaneously. The gate time of photon counter for luminescence measurement was set to 10 ms. For the measurement of luminescence spectra, emitted light was focused on the entrance slit of the spectrometer and measured with an optical multichannel
analyzer. Time-resolved photoluminescence (PL) spectra from MgO crystal were measured and compared with fractoluminescence spectra. 5 eV photons of KrF excimer laser (MPB Technology PSX-100) were irradiated to the sample, and PL was measured with the optical multichannel analyzer attached to the spectrometer. The ratio of the gate width to the delay time was ®xed to 1/5. Details of the experimental setup are described elsewhere [6±8]. Fig. 1 shows time response of fractoemission at bending fracture of single crystal MgO at 1.3 £ 10 25 Pa. Negative charge emission, positive charge emission, and luminescence start at the instant of bending fracture of the sample. Large emission of negative charge lasts about 10 ms after fracture, and small emission continues several hundreds of milliseconds. Bursts of positive charge emission are observed intermittently within several tens of milliseconds after fracture. While, luminescence peaks at fracture, and decays within several milliseconds. Time-response of fractoluminescence in MgO is shown semi-logarithmically in Fig. 2. The solid line is a result of curve ®tting with a sum of two exponential decay functions, I t
2 X i1
Ai £ exp2t=ti :
1
The decay times are about several microseconds and several hundreds of microseconds, respectively. It should be remarked that the decay time of the fast component is just
0038-1098/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00413-0
18
Y. Kawaguchi / Solid State Communications 117 (2001) 17±20
Table 1 Impurity contents in MgO samples (in wt. ppm) Na and K
Ca
Al
Fe
Si
S
Cl
F
Cr
V
Mn
Ni
Ti
Zn
B
P
C
5
40
15
50
10
5
7
3
10
3
4
3
2
1
5
2
10
the same order with the time resolution in the present experiment. Fig. 3 shows fractoluminescence spectra of MgO. Because of the wide slit width for maximum ef®ciency of detecting light, the bandwidth of the measurement system is as large as 20 nm. A very large emission band centered at about 730 nm is observed. Another emission band is situated around 400±500 nm, though very weak and the central wavelength is not clear. Fig. 4 shows time response of fractoluminescence with and without an optical ®lter transmitting light of only l . 560 nm. The fast decaying component is terribly weakened with the optical ®lter. Thus, the wavelength of the fast decaying emission must be shorter than 560 nm, and the wavelength of the slow decaying emission is longer than 560 nm. This result shows that the 400±500 nm band in the fractoluminescence spectra is the fast decaying emission, and that the 730 nm band is the slow decaying emission. Fig. 5 shows PL spectra in MgO under irradiation of KrF
Fig. 1. Time response of fractoemission at bending fracture of MgO in a vacuum: (a) negative charge; (b) positive charge; (c) luminescence; (d) load.
Fig. 2. Time-response of fractoluminescence in MgO with a semilogarithmic scale: dots-experimental data; solid line-result of curve ®tting.
excimer laser, and time-resolved PL spectra are shown in Fig. 6. Initially, the 500 nm band is seen within 1 ms of the delay, and then the 430 nm band appears around 5±10 ms of the delay. Another band around 730±750 nm grows from 5±10 ms of the delay, and is accompanied by a ®ne structure around 1 ms of the delay. This ®ne structure is just due to Cr 31 impurity as discussed below [16]. Four models are proposed for the mechanism of fractoluminescence [6,11]: (i) relaxation luminescence of excited ions emitted from the fracture surface; (ii) discharge of the ambient gas; (iii) blackbody radiation due to local heating of
Fig. 3. Fractoluminescence spectra in MgO: (a) VIS region; (b) VIS±IR region.
Y. Kawaguchi / Solid State Communications 117 (2000) 17±20
19
Fig. 4. Time-response of fractoluminescence in MgO: solid linewithout an optical ®lter; dotted line-with an optical ®lter cutting light of l , 560 nm.
the fracture surface; (iv) relaxation luminescence of defect centers created and excited by mechanical fracture. As shown in Fig. 1, time response of luminescence upon bending fracture of MgO is much different from that of positive and negative charge emission. Thus, the ®rst possibility is not accepted. Moreover, the possibility of gas discharge is denied because our experiment is done in high vacuum, 10 25 Pa. The possibility of blackbody radiation is also denied because the spectrum of blackbody radiation with similar peak wavelength is several times broader than that of fractoluminescence and the spectral shape is totally different. The remaining model, relaxation luminescence of defect centers, is reasonable because progress of crack causes bond-breaking and nuclear motion, and promotes release of atoms and ions from the lattice sites, resulting in the creation of defects. Moreover, the movement of the dislocation mechanically excites defects [5].
Fig. 5. PL spectra in MgO by KrF irradiation: (a) VIS region; (b) VIS±IR region.
Fig. 6. Time-resolved PL spectra in MgO by KrF irradiation.
To clarify the defects causing the fractoluminescence, we compared the luminescence with PL. As mentioned in the previous section, fractoluminescence spectrum shows two bands: 400±500 nm and 730 nm. Decay time of the former band is several microseconds or smaller, while that of the latter band is several hundred microseconds. While, PL spectrum consists of mainly three bands: 500 nm band which peaks within 1 ms, 430 nm band which peaks around 5±10 ms, and 730 nm band which peaks around several hundreds of microsecond. Peak position and the order of the decay time of the 730 nm band in PL agree well with those in fractoluminescence, so that the origin of that band must be the same. Fine structure on the 730 nm band is not observed in fractoluminescence spectrum because of the wide slit width and low resolution of the wavelength on the fractoluminescence measurement. Chao [16] reported a red band which peaks at about 700 nm with vibrational sidebands lines in thermoluminescence spectrum of MgO, and assigned the band to Cr 31 impurity. On the PL spectra which we observed, the 730 nm band also shows vibrational sidebands though the structure is not so clear due to the lack of the spectral resolution in our spectrometer. Because of the similarity of the peak position and the structure, the 730 nm band in the PL of MgO in our study should be also due to Cr 31 impurity center. Thus, the 730 nm band in the fractoluminescence of MgO is also assigned to the relaxation luminescence of Cr 31 impurity excited by mechanical stress during fracture and crack propagation. As for the 400±500 nm band in fractoluminescence of MgO, the peak position is not clearly speci®ed because of
20
Y. Kawaguchi / Solid State Communications 117 (2001) 17±20
the very small intensity, but the decay time of the band is several microseconds or smaller. In PL, the 500 nm band peaks within 1 ms while the 430 nm band peaks around 5±10 ms. The time response of these two band in PL agrees well within the experimental accuracy with the 400±500 nm band in fractoluminescence, suggesting that the origin of the two are the same. In PL, Rosenblatt and his coworkers [21] reported the 390 and 530 nm bands in time-resolved spectra of MgO with different defect densities, and attributed the bands to F 1 and F center, respectively. The peak positions of the two bands were shifted to several tens of nm depending on the densities of defects, and the 500 nm band peaks within 1 ms while the 390 nm band peaks around 1 ms, depending on the sample conditions. Considering the ambiguity due to the difference of the sample, the two bands on Rosenblatt's work resemble the 430 and 500 nm bands in PL spectra in our study. Thus, the origins of the two bands in PL in our study can be also attributed to F 1 and F centers, and the 400±500 nm band in fractoluminescence may be also assigned to the same defect centers. Upon fracture, ejection of oxygen atoms and ions and creation of oxygen vacancies are expected, and electrons released during fracture will be trapped to the oxygen vacancies resulting in the creation of excited F-type centers. These F-type centers should cause the 400±500 nm emission in fractoluminescence. In summary, luminescence spectra upon bending fracture of MgO crystal in vacuum are investigated. 1. Two emission bands are observed: a large band at about 730 nm; and a weak one around 400±500 nm. 2. The peak position and time response of two fractoluminescence bands are similar to those of PL bands in MgO. 3. The 730 nm band is assigned to be due to Cr 31 impurity, while the 400±500 nm band may be assigned to F-type centers.
References [1] J.T. Dickinson, L.C. Jensen, M.R. McKay, J. Vac. Sci. Technol. A 4 (1986) 1648. [2] J.T. Dickinson, L.C. Jensen, M.R. McKay, J. Vac. Sci. Technol. A 5 (1987) 1162. [3] S.C. Langford, J.T. Dickinson, L.C. Jensen, J. Appl. Phys. 62 (1987) 1437. [4] G.P. Williams Jr., T.J. Turner, Solid State Commun. 29 (1979) 201. [5] T. Hagihara, Y. Hayashiuchi, Y. Kojima, Y. Yamamoto, S. Ohwaki, T. Okada, Phys. Lett. A 137 (1989) 213. [6] Y. Kawaguchi, Phys. Rev. B 52 (1995) 9224. [7] Y. Kawaguchi, Phys. Rev. B 56 (1996) 9721. [8] Y. Kawaguchi, Jpn. J. Appl. Phys. 37 (1998) 1892. [9] P. Varotsos, K. Alexopoulos, Techtonophysics 110 (1984) 99. [10] Y. Enomoto, H. Hashimoto, Electromagnetic Phenomena Related to Earthquake Prediction, Terra Science Publishing Company, Tokyo, 1994, p. 261. [11] Y. Enomoto, H. Hashimoto, Nature 346 (1990) 641. [12] Y. Kawaguchi, Proc. 12th Inter. Symp. Exoemission and its Applications, Polanica, 1997, p. 221. [13] Y. Kawaguchi, Jpn. J. Appl. Phys. 37 (1998) 3495. [14] W.A. Sibley, J.L. Kolopus, W.C. Mallard, Phys. Status Solidi 31 (1969) 223. [15] L.A. Kappers, R.L. Kroes, E.B. Hensley, Phys. Rev. B 10 (1970) 4151. [16] C.-C. Chao, J. Phys. Chem. Solids 32 (1971) 2517. [17] R.D. Newton, W.A. Sibley, Phys. Status Solidi A 41 (1977) 569. [18] R.T. Williams, J.W. Williams, T.J. Turner, K.H. Lee, Phys. Rev. B 20 (1979) 1687. [19] G.P. Summers, T.M. Wilson, B.T. Jeffries, H.T. Tohver, Y. Chen, M.M. Abraham, Phys. Rev. B 27 (1983) 1283. [20] I. Fernandez, J. Llopis, Phys. Status Solidi A 108 (1988) K163. [21] G.H. Rosenblatt, M.W. Rowe, G.P. Williams Jr., R.T. Williams, Y. Chen, Phys. Rev. B 39 (1989) 10309. [22] J.L. Grant, R. Cooper, P. Zeglinski, J.F. Boas, J. Chem. Phys. 90 (1989) 807.