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EPR study of the E′4 center in α-quartz
Solid State Communications, Vol. 30, pp. 575—579. Pergamon Press Ltd. 1979. Printed in Great Britain. EPR STUDY OF THE E~CENTER IN a-QUARTZ L.E. Halliburton,1 BD. Perlson,2 R.A. Weeks,3 J.A. Weil2* and M.C. Wintersgill1 ‘Dept. of Physics, Oklahoma State Univ., Stiliwater, OK 74074, U.S.A. 2Dept. of Chemistry and Chem. Eng., Univ. of Saskatchewan, Saskatoon, Sask.. S7N OWO, Canada
and 3Solid State Division, Oak Ridge National Lab., Oak Ridge, TE 37830, U.S.A. (Received 18 December 1978 by R.H. Silsbee) Electron paramagnetic resonance measurements of the E~center in a-quartz have now proven that this species contains one unpaired electron (S = 1/2), with hyperfme splittin~from one proton (I = 1/2). The spinHamiltonian matrices~and A (H ) have been measured at room temperature. 1. INTRODUCTION WEEKS AND NELSON [1] were the first to describe the paramagnetic center they named E~,created by y.irradiation of a-quartz. The room temperature electron paralnagnetic resonance (EPR) spectrum at X-band consisted of four (virtually) equally spaced and equally intense lines, tentatively suggested to arise from an unpaired electron interacting with an alkali ion (spin I = 3/2, Na23 or Li7). No spin-Hamiltonian was given. A recent note by Haberlandt [2] suggested that the E~ EPR spectrum should be fitted to a spin-Hamiltonian with electron spin S = 3/2. We have now made more detailed EPR measurements [3] and present results thereof, which prove that the E~center ~ = 1/2, with hyperfine splittings arising from one hydrogen nucleus (I = 1/2).
that of the sample described above. This sample (X-rayed but not electron irradiated) was used to confirm the essential features ofthe spectral characteristics of the E, center. To our knowledge, observation of the E, center in natural quartz has not been previously reported. After thermally bleaching both the Clevite crystal
and the natural rose quartz crystal for two hours at 725 K, no EPR absorptions were observable in either sample at 300 of these to Co~7-rays at or 27515orK.atExposure 300 K (total dose samples 200 Mrad) “~
gave rise to paramagnetic centers E~and E~.The former center is described elsewhere [1, 4, 5]. Similarly, use of
,
2. EXPERIMENTAL The principal crystal used in this study is a hydrothermally grown crystal, synthesized by the Clevite Corporation and used as a rectangular plate with dimensions l~= 1.5,12 = 1.0,13 = 0.2cm with Ij (essentially) parallel to one (~ a 1) of the three crystallographic two-fold axes, and 13 along the three-fold screw axis (c) of symmetry. This plate,which had been 2 electron irradiated 1.5 by ~zA cm for for 10 hr), was from(1.7 theMeV sameelectrons, crystal used Weeks earlier E’ studies. The polarity ofthe a, -axis was determined by measuring the sign of the voltage developed on compression along this direction. The crystal was determined to be right a-quartz. A second specimen used is a natural rose quartz crystal (origin Madagascar), with geometry similar to *
Authors to whom enquiries may be addressed. 575
X-rays (30 miii, W-target at 50 mA, 50kV) also gave rise to these species. Further studies revealed that the E~and E~centers were produced by electron irradiation (1.5 MeV, I pAcm2 for 5 mm) at 300Km Electronic Grade and Premium Q crystals synthesized by Sawyer. Prior to the electron irradiation, the as-received Sawyer samples showed no EPR absorptions. The E~center appears stable indefmitely at room temperature, in the dark. However, exposure to ultraviolet light at room temperature caused rapid disappearance of the center. 3. RESULTS AND ANALYSIS For B Ic, the EPR spectrum of the E~center taken at X-band is ifiustrated in the upper portion of Fig. 1 and consists of the four primary absorption lines described previously. A detailed examination of this high symmetry E~spectrum was made at a microwave frequency of 9850.827 MHz where the resonance fields are 350.986, 351.481, 351.968 and 352.464mT. The center of the spectrum is found at hV/f3eB =2.00 106. The near equality of the X-band spacings of the four
EPR STUDY OF THE E~CENTER IN a-QUARTZ
576
Vol. 30, No.9 F-
I
O.4mT
9.1 GH z
L
~
-
_______________
B~
I___________
20.4 GHz
___________
_______
~
Fig. 1. Room temperature EPR spectrum of the E~center in a-quartz for B II c. The upper trace was taken at 9.1 GHz and the lower trace was taken at 20.4 GHz. Although present in the sample, the two lines (separated by approximately 004 mT) attributed to the E~center have been removed from the figure thus leaving a small gap near the center of both traces.
Table 1. The experimental spin-Hwniltonian matrices of the E? center in right a-quartz at room temperalure. See [7] for definitions of 0 and The uncertainty is ±0.00003 for the gmatrix elements and ±0.001 mT for the hyperflne matrix elements ~.
Principal values
Matrices
Principal directions
o R
2.00071
0.00019 2.00101
0.547
0.567 0.725
2.00154 2.00065 2.00060
133.7° 123.0 61.6
53.8° 285.4 354.9
—0.676
0.602
1.886 0.065
126.8 99.8
49.0 311.7
0.674
—0.005
141.5
209.2
—
(mT)
0.00017 0.00043 2.00106 —
Coordinate system: right-handed Cartesian coordinate system; xlIa, (positive x develops negative charge on compression along x); zIIc. Constants:
g0
= 2.0023 193; 1. fl~=9.274096x 10~JT
Vol. 30, No.9
EPR STUDY OF THE E~CENTER IN a-QUARTZ
M:+~,
/
I I
577
(2—4)
E (I__4~..j
M:_h/2
/
m~+/~
LII (I
m ELECTRON ZEEMAN: H’ZEEMAN: H’ HYPERFINE:
>0 0 0
=
—
3)
—
“2
>0 *0 0
>0 *0 * 0
Fig. 2. Energy level scheme for a system S = 1/2,! = 1/2 at a fixed magnetic field B (see [6] for definitions of M,m). adjacent lines suggested [1] that the spectrum might arise from a species with S = 1/2, with the four-line structure attributable to hyperfine interactions with an I = 3/2 nucleus. However, close examination of the spectrum does show that there are measurable differences of the peak-to-peak amplitudes of the lowest and highest field lines as compared to the other two lines (all four lines have the same first derivative linewidth of
0.008 mT). For low microwave power levels, the intensity ratio of the outer pair to inner pair is approximately 1.2:1 at 9850.827 MHz. This is not consistent with an S = 1/2, I = 3/2 species. The true nature of the E,~spin system becomes evident when a detailed angular dependence study of the spectrum is made at X.band. As the crystal is rotated away from B lIc about a twofold axis a
1 normal to B, the four-line spectrum breaks up into 3 spectra with four primary lines each. Labeling the four lines in a given set a, b, c and d, respectively from lowest to highest field, we observe that as the separation of lines b and c decreases (compared with the separation at B c), the intensities ofthese two lines increase and remain equal, while the intensities of lines a and d correspondingly decrease and remain equal. Further, as the splitting between lines b and c approaches zero, lines
a and d are separated by 1.05 mT. This spacing is very nearly twice the proton Larmor frequency (i.e. 2.gii’ ~nB/goj3e= 1.07 mT at B = 351.65 ml). Therefore, we conclude that E~has S = 1/2 and that the hyperfine structure arises from interaction with a proton (I = 1/2) in a situation permitting observation of all 2S(21 + 1)2 possible EPR transitions. Additional work at K-band confirms the conclusion that the E~center is an S = 1/2,1 = 1/2 spin system. As expected, the near equality of the amplitudes and spacings ofthe four primary absorption lines observed at X-band is not found when the spectrum is taken at 20.4 GHz with Blic (see the lower portion of Fig. 1). Also, to a first order approximation, the separation of the outer pair of lines does scale with the magnetic field and thus with the proton Larmor frequency. The spin-Hamiltonian
~
— —
B + f3~ g• S -
~
—
AH’
B I
—
H’
g11’
~
H’
describes the primary spectra of the E~center. The first term (~C,)in the Hamiltonian represents the direct effect of the external magnetic field B on the electron spin S, the second term (WA) treats the interactions between S and the nuclear spin ‘H’ while the last term takes into account the direct effect of B on ‘H’S
578
EPR STUDY OF THE E~CENTER IN a-QUARTZ 0.5—
Vol. 30, No.9
~
0.4-
~
(2—3)
0.3-
4-
:.:
0.2-
•
(2—4) 0.1-
0.0 ~
352.0 351.5
351.0
/~1!3)
—
~ ,
0
~_._._.__(1__4) I
30
60
90 11
120
150
180
(deg.)
Fig. 3. The relative intensities (upper) and line positions (lower) for BIa, lB1 and fixed frequency v = 9.8505 GHz, for site I of the E, center at room temperature. The labels are defmed in Fig. 2. The curves are calculated from the data in Table 1; circles are experimental points. Angle ~1= 0 occurs at Blic. Analysis of EPR data is normally carried out satisfactorily by perturbation techniques assuming ~A ~g~’ However, we are faced here with a situation where the terms ~WAand ~Cg~1 are, in general, equally important. This relaxes the usual EPR selection rules [6] so that all 2S(21 + 1)2 EPRtransitions may be observable (depending on the anisotropy ofAH’ and ~ and on B). Using X-band data, we obtained an estimate of AH’ following the procedure outlined by Weil and Anderson [6] while an estimate ofg was obtained from calculations of the angular dependence ofthe center of spectral lines from each symmetry related site. These estimates, together with the measured spectral line positions and corresponding microwave frequencies were used as input to a best-fitting computer program ~‘
~‘
.
,
employing exact matrix diagonalization [7]. The best-fit principal values and principal vectors of the hydrogen hyperfine coupling and Zeeman splitting matrices, taken to be symmetric, are given in Table 1 and reproduce the measured X-band spectral line positions (19 angles and 188 positions; rotation about a twofold axis) to a mean field deviation of ±0.0015 mT. The matrices given describe the magnetic behavior of one of the six symmetry-related sites observed with point group D3 appropriate for a-quartz [7]. Similar computations based on the K-band data give principal values and principal vectors which agree within experimental error with the X-band results. To corroborate that the observed splittings are due to hyperfine interactions with a proton, we have calculated (for a spectrometer frequency of9850.5 MHz) the
Vol. 30, No.9
EPR STUDY OF THE E~CENTER IN a-QUARTZ 579 R.A.W.), and the171U.S. AirDeputy Force under contract relative intensities (~ (Mm I S~IM’m5 12) of 9.11 F19628-77-C-0 with for Electronic 2S(21 + 1)2 EPR transitions (see Fig. 2 for labeling of Technology (RADC/ET) and monitored by Dr. Alton these transitions) for B in a plane perpendicular to a Armington, Hanscom AFB, Boston (for L.E.H. and twofold axis. These data are presented in Fig. 3 for the M.C.W.) is gratefully acknowledged. matrices in Table 1 (symmetry site 1) together with the experimentally observed intensities (excitation field B1 ha1). Figure 3 also includes the experimentally REFERENCES observed spectral line positions, extrapolated to exactly v = 9850.5 MHz, and the “best-fit” calculated line 1. R.A. Weeks & C.M. Nelson, J. Am. Ceram. Soc. 43, 399Haberlandt,Int. (1960). positions at this same frequency. We see that the agree2. H. Wiss. Kollog., Tech. ment is excellent and the four-line appearance of equal Hochschule Ilmenau (East Germany) 20, 13 spacing and intensity at X-band for Bhic is coincidental. Further studies, including analysis of the weak superhyperfine structure arising from low-abundance ~j29 nuclei, will be reported later.
3.
Phys. Soc. 23, 254 (1978). 4.
Acknowledgements We are pleased to thank 5. Dr. J. Isoya for helpful discussions. Support of this work by the National Research Council of Canada (for B.D.P. 6. and J.A.W.), Oak Ridge National Laboratory operated by Union Carbide Corporation under contract W-74057. eng-26 with the U.S. Department of Energy (for —
(1975). Some of these results were presented at the March APS meeting:W.A. L.E.Sibley Halliburton, M.C. Wuntersgill, J.J. Martin, & R.A. Weeks, BulL Am. R.A. Weeks, Phys. Rev. 130, 570 (1963). J.G. Castle, D.W. Feldman, P.G. Klemens & R.A. Weeks, Phys. Rev. 130, 577 (1963). J.A. Weil & J.H. Anderson,). Chem. Phys. 35, 1410 (1961). H. Rinneberg & J.A. Weil,J. Chem. Phys. 56, 2019 (1971).
and 3Solid State Division, Oak Ridge National Lab., Oak Ridge, TE 37830, U.S.A. (Received 18 December 1978 by R.H. Silsbee) Electron paramagnetic resonance measurements of the E~center in a-quartz have now proven that this species contains one unpaired electron (S = 1/2), with hyperfme splittin~from one proton (I = 1/2). The spinHamiltonian matrices~and A (H ) have been measured at room temperature. 1. INTRODUCTION WEEKS AND NELSON [1] were the first to describe the paramagnetic center they named E~,created by y.irradiation of a-quartz. The room temperature electron paralnagnetic resonance (EPR) spectrum at X-band consisted of four (virtually) equally spaced and equally intense lines, tentatively suggested to arise from an unpaired electron interacting with an alkali ion (spin I = 3/2, Na23 or Li7). No spin-Hamiltonian was given. A recent note by Haberlandt [2] suggested that the E~ EPR spectrum should be fitted to a spin-Hamiltonian with electron spin S = 3/2. We have now made more detailed EPR measurements [3] and present results thereof, which prove that the E~center ~ = 1/2, with hyperfine splittings arising from one hydrogen nucleus (I = 1/2).
that of the sample described above. This sample (X-rayed but not electron irradiated) was used to confirm the essential features ofthe spectral characteristics of the E, center. To our knowledge, observation of the E, center in natural quartz has not been previously reported. After thermally bleaching both the Clevite crystal
and the natural rose quartz crystal for two hours at 725 K, no EPR absorptions were observable in either sample at 300 of these to Co~7-rays at or 27515orK.atExposure 300 K (total dose samples 200 Mrad) “~
gave rise to paramagnetic centers E~and E~.The former center is described elsewhere [1, 4, 5]. Similarly, use of
,
2. EXPERIMENTAL The principal crystal used in this study is a hydrothermally grown crystal, synthesized by the Clevite Corporation and used as a rectangular plate with dimensions l~= 1.5,12 = 1.0,13 = 0.2cm with Ij (essentially) parallel to one (~ a 1) of the three crystallographic two-fold axes, and 13 along the three-fold screw axis (c) of symmetry. This plate,which had been 2 electron irradiated 1.5 by ~zA cm for for 10 hr), was from(1.7 theMeV sameelectrons, crystal used Weeks earlier E’ studies. The polarity ofthe a, -axis was determined by measuring the sign of the voltage developed on compression along this direction. The crystal was determined to be right a-quartz. A second specimen used is a natural rose quartz crystal (origin Madagascar), with geometry similar to *
Authors to whom enquiries may be addressed. 575
X-rays (30 miii, W-target at 50 mA, 50kV) also gave rise to these species. Further studies revealed that the E~and E~centers were produced by electron irradiation (1.5 MeV, I pAcm2 for 5 mm) at 300Km Electronic Grade and Premium Q crystals synthesized by Sawyer. Prior to the electron irradiation, the as-received Sawyer samples showed no EPR absorptions. The E~center appears stable indefmitely at room temperature, in the dark. However, exposure to ultraviolet light at room temperature caused rapid disappearance of the center. 3. RESULTS AND ANALYSIS For B Ic, the EPR spectrum of the E~center taken at X-band is ifiustrated in the upper portion of Fig. 1 and consists of the four primary absorption lines described previously. A detailed examination of this high symmetry E~spectrum was made at a microwave frequency of 9850.827 MHz where the resonance fields are 350.986, 351.481, 351.968 and 352.464mT. The center of the spectrum is found at hV/f3eB =2.00 106. The near equality of the X-band spacings of the four
EPR STUDY OF THE E~CENTER IN a-QUARTZ
576
Vol. 30, No.9 F-
I
O.4mT
9.1 GH z
L
~
-
_______________
B~
I___________
20.4 GHz
___________
_______
~
Fig. 1. Room temperature EPR spectrum of the E~center in a-quartz for B II c. The upper trace was taken at 9.1 GHz and the lower trace was taken at 20.4 GHz. Although present in the sample, the two lines (separated by approximately 004 mT) attributed to the E~center have been removed from the figure thus leaving a small gap near the center of both traces.
Table 1. The experimental spin-Hwniltonian matrices of the E? center in right a-quartz at room temperalure. See [7] for definitions of 0 and The uncertainty is ±0.00003 for the gmatrix elements and ±0.001 mT for the hyperflne matrix elements ~.
Principal values
Matrices
Principal directions
o R
2.00071
0.00019 2.00101
0.547
0.567 0.725
2.00154 2.00065 2.00060
133.7° 123.0 61.6
53.8° 285.4 354.9
—0.676
0.602
1.886 0.065
126.8 99.8
49.0 311.7
0.674
—0.005
141.5
209.2
—
(mT)
0.00017 0.00043 2.00106 —
Coordinate system: right-handed Cartesian coordinate system; xlIa, (positive x develops negative charge on compression along x); zIIc. Constants:
g0
= 2.0023 193; 1. fl~=9.274096x 10~JT
Vol. 30, No.9
EPR STUDY OF THE E~CENTER IN a-QUARTZ
M:+~,
/
I I
577
(2—4)
E (I__4~..j
M:_h/2
/
m~+/~
LII (I
m ELECTRON ZEEMAN: H’ZEEMAN: H’ HYPERFINE:
>0 0 0
=
—
3)
—
“2
>0 *0 0
>0 *0 * 0
Fig. 2. Energy level scheme for a system S = 1/2,! = 1/2 at a fixed magnetic field B (see [6] for definitions of M,m). adjacent lines suggested [1] that the spectrum might arise from a species with S = 1/2, with the four-line structure attributable to hyperfine interactions with an I = 3/2 nucleus. However, close examination of the spectrum does show that there are measurable differences of the peak-to-peak amplitudes of the lowest and highest field lines as compared to the other two lines (all four lines have the same first derivative linewidth of
0.008 mT). For low microwave power levels, the intensity ratio of the outer pair to inner pair is approximately 1.2:1 at 9850.827 MHz. This is not consistent with an S = 1/2, I = 3/2 species. The true nature of the E,~spin system becomes evident when a detailed angular dependence study of the spectrum is made at X.band. As the crystal is rotated away from B lIc about a twofold axis a
1 normal to B, the four-line spectrum breaks up into 3 spectra with four primary lines each. Labeling the four lines in a given set a, b, c and d, respectively from lowest to highest field, we observe that as the separation of lines b and c decreases (compared with the separation at B c), the intensities ofthese two lines increase and remain equal, while the intensities of lines a and d correspondingly decrease and remain equal. Further, as the splitting between lines b and c approaches zero, lines
a and d are separated by 1.05 mT. This spacing is very nearly twice the proton Larmor frequency (i.e. 2.gii’ ~nB/goj3e= 1.07 mT at B = 351.65 ml). Therefore, we conclude that E~has S = 1/2 and that the hyperfine structure arises from interaction with a proton (I = 1/2) in a situation permitting observation of all 2S(21 + 1)2 possible EPR transitions. Additional work at K-band confirms the conclusion that the E~center is an S = 1/2,1 = 1/2 spin system. As expected, the near equality of the amplitudes and spacings ofthe four primary absorption lines observed at X-band is not found when the spectrum is taken at 20.4 GHz with Blic (see the lower portion of Fig. 1). Also, to a first order approximation, the separation of the outer pair of lines does scale with the magnetic field and thus with the proton Larmor frequency. The spin-Hamiltonian
~
— —
B + f3~ g• S -
~
—
AH’
B I
—
H’
g11’
~
H’
describes the primary spectra of the E~center. The first term (~C,)in the Hamiltonian represents the direct effect of the external magnetic field B on the electron spin S, the second term (WA) treats the interactions between S and the nuclear spin ‘H’ while the last term takes into account the direct effect of B on ‘H’S
578
EPR STUDY OF THE E~CENTER IN a-QUARTZ 0.5—
Vol. 30, No.9
~
0.4-
~
(2—3)
0.3-
4-
:.:
0.2-
•
(2—4) 0.1-
0.0 ~
352.0 351.5
351.0
/~1!3)
—
~ ,
0
~_._._.__(1__4) I
30
60
90 11
120
150
180
(deg.)
Fig. 3. The relative intensities (upper) and line positions (lower) for BIa, lB1 and fixed frequency v = 9.8505 GHz, for site I of the E, center at room temperature. The labels are defmed in Fig. 2. The curves are calculated from the data in Table 1; circles are experimental points. Angle ~1= 0 occurs at Blic. Analysis of EPR data is normally carried out satisfactorily by perturbation techniques assuming ~A ~g~’ However, we are faced here with a situation where the terms ~WAand ~Cg~1 are, in general, equally important. This relaxes the usual EPR selection rules [6] so that all 2S(21 + 1)2 EPRtransitions may be observable (depending on the anisotropy ofAH’ and ~ and on B). Using X-band data, we obtained an estimate of AH’ following the procedure outlined by Weil and Anderson [6] while an estimate ofg was obtained from calculations of the angular dependence ofthe center of spectral lines from each symmetry related site. These estimates, together with the measured spectral line positions and corresponding microwave frequencies were used as input to a best-fitting computer program ~‘
~‘
.
,
employing exact matrix diagonalization [7]. The best-fit principal values and principal vectors of the hydrogen hyperfine coupling and Zeeman splitting matrices, taken to be symmetric, are given in Table 1 and reproduce the measured X-band spectral line positions (19 angles and 188 positions; rotation about a twofold axis) to a mean field deviation of ±0.0015 mT. The matrices given describe the magnetic behavior of one of the six symmetry-related sites observed with point group D3 appropriate for a-quartz [7]. Similar computations based on the K-band data give principal values and principal vectors which agree within experimental error with the X-band results. To corroborate that the observed splittings are due to hyperfine interactions with a proton, we have calculated (for a spectrometer frequency of9850.5 MHz) the
Vol. 30, No.9
EPR STUDY OF THE E~CENTER IN a-QUARTZ 579 R.A.W.), and the171U.S. AirDeputy Force under contract relative intensities (~ (Mm I S~IM’m5 12) of 9.11 F19628-77-C-0 with for Electronic 2S(21 + 1)2 EPR transitions (see Fig. 2 for labeling of Technology (RADC/ET) and monitored by Dr. Alton these transitions) for B in a plane perpendicular to a Armington, Hanscom AFB, Boston (for L.E.H. and twofold axis. These data are presented in Fig. 3 for the M.C.W.) is gratefully acknowledged. matrices in Table 1 (symmetry site 1) together with the experimentally observed intensities (excitation field B1 ha1). Figure 3 also includes the experimentally REFERENCES observed spectral line positions, extrapolated to exactly v = 9850.5 MHz, and the “best-fit” calculated line 1. R.A. Weeks & C.M. Nelson, J. Am. Ceram. Soc. 43, 399Haberlandt,Int. (1960). positions at this same frequency. We see that the agree2. H. Wiss. Kollog., Tech. ment is excellent and the four-line appearance of equal Hochschule Ilmenau (East Germany) 20, 13 spacing and intensity at X-band for Bhic is coincidental. Further studies, including analysis of the weak superhyperfine structure arising from low-abundance ~j29 nuclei, will be reported later.
3.
Phys. Soc. 23, 254 (1978). 4.
Acknowledgements We are pleased to thank 5. Dr. J. Isoya for helpful discussions. Support of this work by the National Research Council of Canada (for B.D.P. 6. and J.A.W.), Oak Ridge National Laboratory operated by Union Carbide Corporation under contract W-74057. eng-26 with the U.S. Department of Energy (for —
(1975). Some of these results were presented at the March APS meeting:W.A. L.E.Sibley Halliburton, M.C. Wuntersgill, J.J. Martin, & R.A. Weeks, BulL Am. R.A. Weeks, Phys. Rev. 130, 570 (1963). J.G. Castle, D.W. Feldman, P.G. Klemens & R.A. Weeks, Phys. Rev. 130, 577 (1963). J.A. Weil & J.H. Anderson,). Chem. Phys. 35, 1410 (1961). H. Rinneberg & J.A. Weil,J. Chem. Phys. 56, 2019 (1971).