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Asymmetry in the local structural order in arsenic chalcogenide glasses: High field NMR in crystalline and glassy As2Se3
Solid State Communications, Vol. 104, No. 11,pp.669-672, 1997 0 1997 Published by Elsevier Science Ltd Printed in Great Britain OO38-1098/97 $17.00+.00
PIk SOO38-1098(97)10007-2
ASYMMETRY
IN THE LOCAL STRUCTURAL ORDER IN ARSENIC CHALCOGENIDE HIGH FIELD NMR IN CRYSTALLINE AND GLASSY AspSes
P. Hari,’ P.C. Taylor,’
A. Kleinhammes,b
P.L. Kuhns,b W.G. Moultonb
GLASSES:
and N.S. Sullivan’
“Physics Department, University of Utah, Salt Lake City, UT 84112, U.S.A. ‘National High Magnetic Field Laboratory, Tallahassee, FL 32306, U.S.A. “Physics Department, University of Florida, Gainesville, FL 32611, U.S.A. (Received and accepted
11 August 1997 by A.L. Efros)
Nuclear magnetic resonance (NMR) of 75As in crystalline and glassy samples of As$es has been studied at magnetic fields up to 22 T. The results, which yield asymmetries in the electric field gradient at the arsenic sites that disagree with those inferred from previous low field studies, are inconsistent with the predictions of a common model (Raft Model) for the structure of glassy AszSe3 and other chalcogenide glasses. This technique should be useful for many other solids that contain one of the twenty elements whose nuclei have spin 3/2 and relatively large quadrupole moment. 0 1997 Published by Elsevier Science Ltd Keywords: A. disordered, C. crystal structure and symmetry, ligand field, E. nuclear resonances.
The structures of the prototypical chalcogenide glasses, As2Ses and As2Ss, have been the subject of some debate for many years. Although the local, nearest-neighbor order is well established, the intermediate range order on a scale of several interatomic spacings is still controversial. For example, there is evidence in these glasses for the presence of twelve-membered ring structure, such as occurs in the layered crystalline compounds, but the ways in which these rings are cross-linked or terminated are not well understood. One well established model, for which there is some experimental support from previous ‘“Te Mossbauer [l] and Zeeman-broadened 75As NQR measurements [2], is the so-called outrigger raft model of Phillips [3]. An important consequence of this model is that a large fraction of the local As pyramidal sites (40%) in the glass are highly distorted from axial symmetry. In the present letter we use crystalline and glassy AssSes as a prototypical example to re-examine the local structural order. Using the broad line NMR measurements to be performed at very high fields (up to 27 T for As2S3 and As), we show that the deductions based on the previous Zeeman-broadened NQR experiments in both glassy [2] and crystalline [4] AszSes are not correct. The new studies reported here show that the vast majority of the As sites are nearly axially symmetric in both the glass and the crystal. This result casts doubt on the validity of
D. crystal and
the raft model as an accurate description of the intermediate range order in these glasses. We also show that high-field, broad line NMR measurements, such as those described in this letter, will be useful in many materials systems involving nuclei with a spin of 312 because the NQR spectra for these systems cannot easily determine the asymmetry of the local sites. The high-field NMR studies can determine the asymmetries and in principle, the distribution of the asymmetries which is important for determining intermediate-range order in glasses. High-field NMR measurements have also been reported recently on magnetic single crystals [5]. High field 75As NMR measurements were performed at the National High Magnetic Field Laboratory (NHMFL) using a 24.5 T, 32 mm bore d.c. magnet and a 30 T magnet, with a homogeneity of 1 part in lo5 over 5 mm. The pulsed NMR spectrometer was operated at approximately 125 MHz which corresponds to a Zeeman field of approximately 17 T for 75As. The frequency of NMR spectrometer was fixed and the magnetic field was varied to produce the NMR spectra. Because the NMR lineshapes in the powdered and glassy samples studied are very broad, the amplitude of the spin echo following a 90”- 180” Hahn echo sequence was monitored as a function of magnetic field. This procedure produced a histogram of the NMR powder pattern [6]. All measurements were
HIGH FIELD NMR IN CRYSTALLINE
670
carried out at 77 K, a temperature at which the signal-tonoise ratio of an individual echo is improved from 300 K but at which the spin-lattice relaxation time T, remains short enough to employ signal averaging techniques effectively. [At 77 K Tt is approximately 0.1 s for the glass and 1 s for the crystal. Repetition rates of 0.5 and 4 s were employed for the glass and crystal, respectively.] Typical 90” pulses were -2 ps. The 75As NMR results on a powdered sample of crystalline AszSe3 are shown in Fig. 1. The solid lines are fits to the data as described below. Figure l(a) presents a survey of the lineshape over
1
160
AND GLASSY
Vol. 104, No. 11
As&
a wide range of magnetic field while Fig. l(b) shows data taken at higher point density over a limited range. Note that the two data sets were taken at slightly different spectrometer operating frequencies. The two distinct arsenic sites in the unit cell [7] are clearly resolved as a splitting in the two singularities [6] in the powder spectrum near 16.8 and 18.4 T. Similar 75As NMR spectra are shown for glassy AszSe3 in Fig. 2. Consistent with earlier nuclear quadrupole 240 t 210
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Fig. 1. 75As high field NMR absorption in crystalline As2Se3. Open circles are experimental data and solid lines are theoretical fits as explained in the text. (a) full spectrum at low resolution at Y, = 125.57 MHz, (b) central region of the spectrum at higher resolution at u, = 127.05 MHz.
Magnetic
Field (Tesla)
Fig. 2. 75As high field NMR absorption in glassy As$es at v = 125.57 MHz. Open circles are experimental data and solid lines are theoretical fits as explained in the text. (a) Full spectrum at low resolution, (b) central region of the spectrum at higher resolution. Dotted line is the prediction of a previous Zeeman-perturbed NQR experiment [2] as explained in the text.
Vol. 104, No. 11
HIGH FIELD NMR IN CRYSTALLINE
resonance (NQR) studies [4], there is no evidence for two distinct sites in the glass. In fact, the NMR intensity in the regions near the two divergences exhibits much less resolution than in the crystalline case. The solid lines are again fits to the data and the dotted line in Fig. 2(b) is the anticipated lineshape from earlier Zeeman perturbed NQR measurements [2] that suggested a bimodal distribution of As sites where approximately 40% of the sites are very asymmetric. The spectra in Figs 1 and 2 can be fit accurately and uniquely by reference to the earlier NQR results. We first examine the case of crystalline AszSeJ where the procedure is simpler. For a nucleus with I = 3/2 there exists one NQR resonant frequency given by
AND GLASSY
A&Se3
671
NQR spectra self consistently, but the very simple procedure (using the NQR line shape and vpp as the initial parameters) employed here provides quite accurate values for and q. The values determined for and r] for the two crystalline sites are 56 MHz and 0.17 and 60 MHZ and 0.12, respectively. Thus both of the sites in the crystal are very nearly axially symmetric. These results are unambiguous, but they are in disagreement with values of 7 determined in earlier Zeemanmodulated NQR measurements [4]. An additional parameter that is determined by the fits shown in Fig. 1 is an estimate of the chemical shift for 75As. The isotropic component of this shift is estimated to be - 1.7 X 103, a value which is consistent with those observed in other arsenic compounds [8]. Similar results are obtained [9] VNQR= VQ(1 + ?72/3)1’2, (1) for the isomorphic crystal As.$Ss. A similar fitting procedure can be employed to find where e2qQ/2h and e is the electronic charge, q the and rl for glassy As$es. The 75As NQR lineshape for maximum component of the electric field gradient at the the glass is inhomogeneously broadened (full width at nuclear site, Q the nuclear quadrupole moment and h half maximum [FWHM] of approximately 4 MHz) [4] Planck’s constant. [Note that equation (1) is an exact compared to the narrow (approximately 50 kHz FWHM) expression and refers to the case where the magnetic crystalline lines. Therefore, for the glass, equations (1) field and hence the Zeeman interaction, is zero.] The and (2) determine the peak values of and 77which are parameter q, which varies between zero and one, is a 58 + 1 MHz and 0.15 2 0.05, respectively. Whereas the measure of the departure of the electric field gradient inhomogeneous broadening indicated by the widths of from axial symmetry. When 7 = 0 the field gradient the crystalline NQR lines is an insignificant factor in is axially symmetric. Because there is only one determining the NMR lineshapes shown in Fig. 1, the NQR transition given by equation (1) for a nucleus influence of the inhomogeneous NQR lineshape of the with I = 3/2, one cannot determine both and 17 glass on the NMR spectrum is important. Therefore the independently. For small values of q (50.3), VNQR is fits shown by the solid lines in Fig. 2 have assumed a insensitive to q and in this case the NQR measurement distribution of commensurate with the known NQR provides a reasonably accurate measurement of lineshape. For simplicity we have assumed that q is Since the two divergences are the most prominent constant, but it is apparent from the NMR spectrum features in the NMR powder spectrum we use the that there can be no significant contribution from sites separation of these two features as a second equation to with large values of 17.Detailed, self-consistent lineshape determine uniquely the values of and 7. For r] < l/3 fittings of the high-field NMR, the NQR and the Zeemanthis separation is given by [6] perturbed NQR spectra, to be published elsewhere, show that the vast majority of the sites (approximately 90%) Avpp = -$(25 - 2217+ r2). must have values ‘of v < 0.2 consistent with the error 0 quoted above. There is also a chemical shift for glassy where v, is the spectrometer operating frequency. For AszSes, as indeed there must be, whose isotropic n > l/3 the equation is different but the procedure is the component is also approximately -1.7 X 10B3. Similar same. The solid line fit to the spectrum in Fig. 1 was conclusions can be drawn from measurements [9] made obtained using and 7 determined by solving equations in glassy As#b. (1) and (2) for each of the two arsenic sites. Even though It is perhaps easy to understand how the As only the separations between the two divergences were pyramidal units in glassy As$es could remain nearly used to determine the initial parameters, the overall fit to axially symmetric because the two-fold-coordinated the entire NMR spectrum is excellent. [The oscillations chalcogen (Se) can provide the bond angle distortions near v, (approximately 17.3 T) in the fits are artifacts of necessary to build a three dimensional network. This the finite grid size used in numerically calculating the situation is exactly analogous to the well defined Si04 powder patterns.] A more accurate fit to the experimental tetrahedra in SiOz and other silicate glasses. However, spectrum is obtained (to be published elsewhere) by there is another prototype amorphous semiconductor, performing a least-squares fit using all the data from amorphous arsenic or a-As, where the pyramidal units the high-field NMR, the NQR and the Zeeman-perturbed must be distorted because all As atoms are three-fold vQ
vQ
vQ
=
vQ
vQ
vQ
vQ.
vQ
vQ
vQ
672
HIGH FIELD NMR IN CRYSTALLINE AND GLASSY AszSe3
High-field NMR measurements in coordinated. amorphous As, when combined with earlier NQR experiments [lo] using the procedure just described, confirm this intuition [9] since in this solid the average value of 7 is 0.5 and very few, if any, sites have 7 C 0.3. As mentioned above, earlier Zeeman-perturbed NQR measurements of Szeftel and Alloul [2] in glassy AszSes found evidence for two distinct sites with q = 0.14 +- 0.07 and 0.45 + 0.14 whose relative weights are 0.6 and 0.4, respectively. [The variances quoted for rl are half-widths of the assumed Gaussian distributions.] The presence of these two sites was inferred from subtle changes in the lineshape. The dashed line in Fig. 2(b) shows the high field NMR lineshape expected from the Szeftel and Alloul parameters (without the distributions whose inclusion will make the fit worse). Although the dashed line fits the gross features of the spectrum, the data are clearly accurate enough to distinguish between the two fits. In particular, note that for the Zeemanperturbed NMR parameters (dashed curve), the widths and separations of the two divergences in the powder pattern are in error as well as the relative heights of the two peaks. [The heights are between 10% and 20% too low and the widths are between 25% and 40% too high.] There are even larger discrepancies when the entire lineshape is considered and when distributions in the values of q, as suggested by Szeftel and Alloul [2], are considered. The disagreement is produced by the large concentration of sites with a large value of 7. The present high field results unambiguously eliminate this possibility. In doing so our results call into question the effectiveness of a model that has often been employed to explain the intermediate range order in chalcogenide glasses - the so-called raft model [3]. The raft model proposes twelve-membered rings whose six As sites are of two distinct types - four that are terminated by chalcogen-chalcogen bonds and two that provide the cross linking to the rest of the structure. The sites that consist of four As atoms per ring are supposed to be relaxed [3] because of the flexibility of the chalcogenchalcogen bonds, but the two cross-linking sites are supposed to be significantly distorted from axial symmetry. From the present NMR measurements we can eliminate such a bimodal distribution where approximately 33% of the As sites strongly depart from axial symmetry. At the very least, the NMR measurements cannot be used as evidence for the existence of ring structures with two distinct As sites. An alternative model that is consistent with the NMR data is to assume that the ring structures or partial ring
Vol. 104, No. 11
structures are cross-linked by a continuous random network of AsSe3 pyramidal units where the “randomness” is primarily in the As-Se-As bond angles. This picture is very similar to modem models for the structure of glassy SiOz. In summary, the first high field, broad-line NMR experiments demonstrate the ability to determine the asymmetry of the electric field gradient at a nuclear site. The technique has solved a long standing problem in arsenic chalcogenide crystals and glasses and placed some severe restrictions on models of the intermediate range order in the prototypical glasses AszSe3 and AS&. These results should stimulate theoretical calculations now that the asymmetries at the arsenic sites are accurately known in these solids. This method should prove useful in a wide range of materials systems which contain nuclei with Z = 3/2. There are approximately 20 such isotopes, of which Cl, Cu, Ga and Gd are important examples. Acknowledgements-Work performed at the NHMFL was supported by NSF under grant number DMR 9527035 and work performed at the University of Utah was supported by NSF under grant number DMR 9403806. One of the authors (PH) gratefully acknowledges a travel grant received from the users fund at the NHMFL. REFERENCES 1. Zitkovsky, I. and Boolchand, P., J. Non-Cryst. Solids, 114, 1989, 70 (and references contained therein). 2. Szeftel, J. and Alloul, H., Phys. Rev. Let& 42, 1979, 5274; Szeftel, J., Philos. Mug., B43, 1981, 549. 3. Phillips, J.C., Phys. Rev., B21, 1979, 12. 4. Rubinstein, M. and Taylor, P.C., Phys. Rev. Lett., 29, 1972, 119; Phys. Rev., B9, 1974,4258. 5. Fagot-Revurat, Y., Horvatic, M., Berthier, C., Segransan, P., Dhalenne, G. and Revcolevschi, A., Phys. Rev. Lett., 77, 1996, 1861. 6. Taylor, P.C., Baugher, J.F. and Kriz, H.M.,-Chem. Rev., 75, 1975, 203. 7. Renninger, A.L. and Averbach, B.L., Acta Cryst., B29,1973, 1583. 8. See for example, Balimann, G. and Pregosin, P.S., J. Mag. Res., 26, 1977, 283. 9. Hari, P., Taylor, P.C., Kleinhammes, A., Kuhns, P.L., Moulton, W.G. and Sullivan, N.S., Unpublished. 10. Jellison, G.E., Petersen, G.L. and Taylor, P.C., Phys. Rev. Lett., 42, 1979, 1413; Phys. Rev., B22, 1980,3903.
PIk SOO38-1098(97)10007-2
ASYMMETRY
IN THE LOCAL STRUCTURAL ORDER IN ARSENIC CHALCOGENIDE HIGH FIELD NMR IN CRYSTALLINE AND GLASSY AspSes
P. Hari,’ P.C. Taylor,’
A. Kleinhammes,b
P.L. Kuhns,b W.G. Moultonb
GLASSES:
and N.S. Sullivan’
“Physics Department, University of Utah, Salt Lake City, UT 84112, U.S.A. ‘National High Magnetic Field Laboratory, Tallahassee, FL 32306, U.S.A. “Physics Department, University of Florida, Gainesville, FL 32611, U.S.A. (Received and accepted
11 August 1997 by A.L. Efros)
Nuclear magnetic resonance (NMR) of 75As in crystalline and glassy samples of As$es has been studied at magnetic fields up to 22 T. The results, which yield asymmetries in the electric field gradient at the arsenic sites that disagree with those inferred from previous low field studies, are inconsistent with the predictions of a common model (Raft Model) for the structure of glassy AszSe3 and other chalcogenide glasses. This technique should be useful for many other solids that contain one of the twenty elements whose nuclei have spin 3/2 and relatively large quadrupole moment. 0 1997 Published by Elsevier Science Ltd Keywords: A. disordered, C. crystal structure and symmetry, ligand field, E. nuclear resonances.
The structures of the prototypical chalcogenide glasses, As2Ses and As2Ss, have been the subject of some debate for many years. Although the local, nearest-neighbor order is well established, the intermediate range order on a scale of several interatomic spacings is still controversial. For example, there is evidence in these glasses for the presence of twelve-membered ring structure, such as occurs in the layered crystalline compounds, but the ways in which these rings are cross-linked or terminated are not well understood. One well established model, for which there is some experimental support from previous ‘“Te Mossbauer [l] and Zeeman-broadened 75As NQR measurements [2], is the so-called outrigger raft model of Phillips [3]. An important consequence of this model is that a large fraction of the local As pyramidal sites (40%) in the glass are highly distorted from axial symmetry. In the present letter we use crystalline and glassy AssSes as a prototypical example to re-examine the local structural order. Using the broad line NMR measurements to be performed at very high fields (up to 27 T for As2S3 and As), we show that the deductions based on the previous Zeeman-broadened NQR experiments in both glassy [2] and crystalline [4] AszSes are not correct. The new studies reported here show that the vast majority of the As sites are nearly axially symmetric in both the glass and the crystal. This result casts doubt on the validity of
D. crystal and
the raft model as an accurate description of the intermediate range order in these glasses. We also show that high-field, broad line NMR measurements, such as those described in this letter, will be useful in many materials systems involving nuclei with a spin of 312 because the NQR spectra for these systems cannot easily determine the asymmetry of the local sites. The high-field NMR studies can determine the asymmetries and in principle, the distribution of the asymmetries which is important for determining intermediate-range order in glasses. High-field NMR measurements have also been reported recently on magnetic single crystals [5]. High field 75As NMR measurements were performed at the National High Magnetic Field Laboratory (NHMFL) using a 24.5 T, 32 mm bore d.c. magnet and a 30 T magnet, with a homogeneity of 1 part in lo5 over 5 mm. The pulsed NMR spectrometer was operated at approximately 125 MHz which corresponds to a Zeeman field of approximately 17 T for 75As. The frequency of NMR spectrometer was fixed and the magnetic field was varied to produce the NMR spectra. Because the NMR lineshapes in the powdered and glassy samples studied are very broad, the amplitude of the spin echo following a 90”- 180” Hahn echo sequence was monitored as a function of magnetic field. This procedure produced a histogram of the NMR powder pattern [6]. All measurements were
HIGH FIELD NMR IN CRYSTALLINE
670
carried out at 77 K, a temperature at which the signal-tonoise ratio of an individual echo is improved from 300 K but at which the spin-lattice relaxation time T, remains short enough to employ signal averaging techniques effectively. [At 77 K Tt is approximately 0.1 s for the glass and 1 s for the crystal. Repetition rates of 0.5 and 4 s were employed for the glass and crystal, respectively.] Typical 90” pulses were -2 ps. The 75As NMR results on a powdered sample of crystalline AszSe3 are shown in Fig. 1. The solid lines are fits to the data as described below. Figure l(a) presents a survey of the lineshape over
1
160
AND GLASSY
Vol. 104, No. 11
As&
a wide range of magnetic field while Fig. l(b) shows data taken at higher point density over a limited range. Note that the two data sets were taken at slightly different spectrometer operating frequencies. The two distinct arsenic sites in the unit cell [7] are clearly resolved as a splitting in the two singularities [6] in the powder spectrum near 16.8 and 18.4 T. Similar 75As NMR spectra are shown for glassy AszSe3 in Fig. 2. Consistent with earlier nuclear quadrupole 240 t 210
140
30 0
20
a
10
12
14
16
Magnetic 0
a
10
12
14
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la
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18.0
18.5
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Fig. 1. 75As high field NMR absorption in crystalline As2Se3. Open circles are experimental data and solid lines are theoretical fits as explained in the text. (a) full spectrum at low resolution at Y, = 125.57 MHz, (b) central region of the spectrum at higher resolution at u, = 127.05 MHz.
Magnetic
Field (Tesla)
Fig. 2. 75As high field NMR absorption in glassy As$es at v = 125.57 MHz. Open circles are experimental data and solid lines are theoretical fits as explained in the text. (a) Full spectrum at low resolution, (b) central region of the spectrum at higher resolution. Dotted line is the prediction of a previous Zeeman-perturbed NQR experiment [2] as explained in the text.
Vol. 104, No. 11
HIGH FIELD NMR IN CRYSTALLINE
resonance (NQR) studies [4], there is no evidence for two distinct sites in the glass. In fact, the NMR intensity in the regions near the two divergences exhibits much less resolution than in the crystalline case. The solid lines are again fits to the data and the dotted line in Fig. 2(b) is the anticipated lineshape from earlier Zeeman perturbed NQR measurements [2] that suggested a bimodal distribution of As sites where approximately 40% of the sites are very asymmetric. The spectra in Figs 1 and 2 can be fit accurately and uniquely by reference to the earlier NQR results. We first examine the case of crystalline AszSeJ where the procedure is simpler. For a nucleus with I = 3/2 there exists one NQR resonant frequency given by
AND GLASSY
A&Se3
671
NQR spectra self consistently, but the very simple procedure (using the NQR line shape and vpp as the initial parameters) employed here provides quite accurate values for and q. The values determined for and r] for the two crystalline sites are 56 MHz and 0.17 and 60 MHZ and 0.12, respectively. Thus both of the sites in the crystal are very nearly axially symmetric. These results are unambiguous, but they are in disagreement with values of 7 determined in earlier Zeemanmodulated NQR measurements [4]. An additional parameter that is determined by the fits shown in Fig. 1 is an estimate of the chemical shift for 75As. The isotropic component of this shift is estimated to be - 1.7 X 103, a value which is consistent with those observed in other arsenic compounds [8]. Similar results are obtained [9] VNQR= VQ(1 + ?72/3)1’2, (1) for the isomorphic crystal As.$Ss. A similar fitting procedure can be employed to find where e2qQ/2h and e is the electronic charge, q the and rl for glassy As$es. The 75As NQR lineshape for maximum component of the electric field gradient at the the glass is inhomogeneously broadened (full width at nuclear site, Q the nuclear quadrupole moment and h half maximum [FWHM] of approximately 4 MHz) [4] Planck’s constant. [Note that equation (1) is an exact compared to the narrow (approximately 50 kHz FWHM) expression and refers to the case where the magnetic crystalline lines. Therefore, for the glass, equations (1) field and hence the Zeeman interaction, is zero.] The and (2) determine the peak values of and 77which are parameter q, which varies between zero and one, is a 58 + 1 MHz and 0.15 2 0.05, respectively. Whereas the measure of the departure of the electric field gradient inhomogeneous broadening indicated by the widths of from axial symmetry. When 7 = 0 the field gradient the crystalline NQR lines is an insignificant factor in is axially symmetric. Because there is only one determining the NMR lineshapes shown in Fig. 1, the NQR transition given by equation (1) for a nucleus influence of the inhomogeneous NQR lineshape of the with I = 3/2, one cannot determine both and 17 glass on the NMR spectrum is important. Therefore the independently. For small values of q (50.3), VNQR is fits shown by the solid lines in Fig. 2 have assumed a insensitive to q and in this case the NQR measurement distribution of commensurate with the known NQR provides a reasonably accurate measurement of lineshape. For simplicity we have assumed that q is Since the two divergences are the most prominent constant, but it is apparent from the NMR spectrum features in the NMR powder spectrum we use the that there can be no significant contribution from sites separation of these two features as a second equation to with large values of 17.Detailed, self-consistent lineshape determine uniquely the values of and 7. For r] < l/3 fittings of the high-field NMR, the NQR and the Zeemanthis separation is given by [6] perturbed NQR spectra, to be published elsewhere, show that the vast majority of the sites (approximately 90%) Avpp = -$(25 - 2217+ r2). must have values ‘of v < 0.2 consistent with the error 0 quoted above. There is also a chemical shift for glassy where v, is the spectrometer operating frequency. For AszSes, as indeed there must be, whose isotropic n > l/3 the equation is different but the procedure is the component is also approximately -1.7 X 10B3. Similar same. The solid line fit to the spectrum in Fig. 1 was conclusions can be drawn from measurements [9] made obtained using and 7 determined by solving equations in glassy As#b. (1) and (2) for each of the two arsenic sites. Even though It is perhaps easy to understand how the As only the separations between the two divergences were pyramidal units in glassy As$es could remain nearly used to determine the initial parameters, the overall fit to axially symmetric because the two-fold-coordinated the entire NMR spectrum is excellent. [The oscillations chalcogen (Se) can provide the bond angle distortions near v, (approximately 17.3 T) in the fits are artifacts of necessary to build a three dimensional network. This the finite grid size used in numerically calculating the situation is exactly analogous to the well defined Si04 powder patterns.] A more accurate fit to the experimental tetrahedra in SiOz and other silicate glasses. However, spectrum is obtained (to be published elsewhere) by there is another prototype amorphous semiconductor, performing a least-squares fit using all the data from amorphous arsenic or a-As, where the pyramidal units the high-field NMR, the NQR and the Zeeman-perturbed must be distorted because all As atoms are three-fold vQ
vQ
vQ
=
vQ
vQ
vQ
vQ.
vQ
vQ
vQ
672
HIGH FIELD NMR IN CRYSTALLINE AND GLASSY AszSe3
High-field NMR measurements in coordinated. amorphous As, when combined with earlier NQR experiments [lo] using the procedure just described, confirm this intuition [9] since in this solid the average value of 7 is 0.5 and very few, if any, sites have 7 C 0.3. As mentioned above, earlier Zeeman-perturbed NQR measurements of Szeftel and Alloul [2] in glassy AszSes found evidence for two distinct sites with q = 0.14 +- 0.07 and 0.45 + 0.14 whose relative weights are 0.6 and 0.4, respectively. [The variances quoted for rl are half-widths of the assumed Gaussian distributions.] The presence of these two sites was inferred from subtle changes in the lineshape. The dashed line in Fig. 2(b) shows the high field NMR lineshape expected from the Szeftel and Alloul parameters (without the distributions whose inclusion will make the fit worse). Although the dashed line fits the gross features of the spectrum, the data are clearly accurate enough to distinguish between the two fits. In particular, note that for the Zeemanperturbed NMR parameters (dashed curve), the widths and separations of the two divergences in the powder pattern are in error as well as the relative heights of the two peaks. [The heights are between 10% and 20% too low and the widths are between 25% and 40% too high.] There are even larger discrepancies when the entire lineshape is considered and when distributions in the values of q, as suggested by Szeftel and Alloul [2], are considered. The disagreement is produced by the large concentration of sites with a large value of 7. The present high field results unambiguously eliminate this possibility. In doing so our results call into question the effectiveness of a model that has often been employed to explain the intermediate range order in chalcogenide glasses - the so-called raft model [3]. The raft model proposes twelve-membered rings whose six As sites are of two distinct types - four that are terminated by chalcogen-chalcogen bonds and two that provide the cross linking to the rest of the structure. The sites that consist of four As atoms per ring are supposed to be relaxed [3] because of the flexibility of the chalcogenchalcogen bonds, but the two cross-linking sites are supposed to be significantly distorted from axial symmetry. From the present NMR measurements we can eliminate such a bimodal distribution where approximately 33% of the As sites strongly depart from axial symmetry. At the very least, the NMR measurements cannot be used as evidence for the existence of ring structures with two distinct As sites. An alternative model that is consistent with the NMR data is to assume that the ring structures or partial ring
Vol. 104, No. 11
structures are cross-linked by a continuous random network of AsSe3 pyramidal units where the “randomness” is primarily in the As-Se-As bond angles. This picture is very similar to modem models for the structure of glassy SiOz. In summary, the first high field, broad-line NMR experiments demonstrate the ability to determine the asymmetry of the electric field gradient at a nuclear site. The technique has solved a long standing problem in arsenic chalcogenide crystals and glasses and placed some severe restrictions on models of the intermediate range order in the prototypical glasses AszSe3 and AS&. These results should stimulate theoretical calculations now that the asymmetries at the arsenic sites are accurately known in these solids. This method should prove useful in a wide range of materials systems which contain nuclei with Z = 3/2. There are approximately 20 such isotopes, of which Cl, Cu, Ga and Gd are important examples. Acknowledgements-Work performed at the NHMFL was supported by NSF under grant number DMR 9527035 and work performed at the University of Utah was supported by NSF under grant number DMR 9403806. One of the authors (PH) gratefully acknowledges a travel grant received from the users fund at the NHMFL. REFERENCES 1. Zitkovsky, I. and Boolchand, P., J. Non-Cryst. Solids, 114, 1989, 70 (and references contained therein). 2. Szeftel, J. and Alloul, H., Phys. Rev. Let& 42, 1979, 5274; Szeftel, J., Philos. Mug., B43, 1981, 549. 3. Phillips, J.C., Phys. Rev., B21, 1979, 12. 4. Rubinstein, M. and Taylor, P.C., Phys. Rev. Lett., 29, 1972, 119; Phys. Rev., B9, 1974,4258. 5. Fagot-Revurat, Y., Horvatic, M., Berthier, C., Segransan, P., Dhalenne, G. and Revcolevschi, A., Phys. Rev. Lett., 77, 1996, 1861. 6. Taylor, P.C., Baugher, J.F. and Kriz, H.M.,-Chem. Rev., 75, 1975, 203. 7. Renninger, A.L. and Averbach, B.L., Acta Cryst., B29,1973, 1583. 8. See for example, Balimann, G. and Pregosin, P.S., J. Mag. Res., 26, 1977, 283. 9. Hari, P., Taylor, P.C., Kleinhammes, A., Kuhns, P.L., Moulton, W.G. and Sullivan, N.S., Unpublished. 10. Jellison, G.E., Petersen, G.L. and Taylor, P.C., Phys. Rev. Lett., 42, 1979, 1413; Phys. Rev., B22, 1980,3903.