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Deuteron and 35Cl spin lattice relaxation in DCl and HCl
Volume 24A,
number
10
PHYSICS
35Cl
DEUTERONAND
SPIN
LETTERS
LATTICE
8 May 1967
RELA-XATION
IN DC1 AND
HCI
J. G. POWLES and M. RHODES* Physics Laboratories.
University of Kent! Canterbuys,
Received
England
1 April 1967
Molecular reorientation in liquid and upper solid phase DC1 is found to be rapid, and probably diffusional.
We report measurements of the nuclear spin lattice relaxation time, Tl, for deuterons in deuterium chloride in the liquid up to the critical temperature and in the higher temperature solid phase tid also the 35C1 T1 for DC1 and HCl. We used the conventional 900, T , go0 pulSe method at 9 MHz [l]. The results are shown in fig. 1 and have been briefly discussed elsewhere [ 21. They differ considerably from results recently reported for the liquid [3] by a method which is not revealed. Some preliminary measurements we have made suggest that Boehme and Eisner may have measured T2 and not Tl. We were unable to observe signals in the lower temperature solid phase. This was expected because the 35C1 pure quadrupole resonance is readily observed [4]. - 100
-150 TEMPERATURE
-50
0
%
I=
_ 100
I
I 10
I
I
6
6
4
Fig. 1. Deuteron (0, left hand ordinates in seconds) and 35c1 (0, right hanh ordinates in microseconds) s in lattice relaxation times in 90% DCl/lO% HCI. Also g5 Cl(X) relaxation times in 75% HC1/25% DCl. DBE and CBE ‘-’ are deuteron and chlorine relaxation times respectively from ref. 3. T.P. , M.P. and C.P. indicate the first order transition, melting and critical temperature respectively.
unaffected
by melting
The strongest nuclear relaxing mechanism is the electric quadrupole (eQ$ interaction with the molecular field gradient (eq) and for sufficiently rapid reorientation of the molecule l/T1 = = c(eqQ/h)2~Q where c = i for spin Z = 1, as for deuterons and c = h for Z = $, as for 35Cl nuclei. TQ is the correlation time for reorientation of the field gradient. The plots of In T1 versus -103/T, where T is the absolute temperature, are parallel straight lines which suggests that TQ has an Arrhenius temperature behaviour with an activation energy of 0.8 k&/mole (0.035 eV/molecule). Cade [5] has calculated that for DC1 (e2qQ/h)3sC1 = 67.9 MHz in agreement with the microwave value [6] 67.3 MHz. He also calculated (e2qQ/k) in DC1 to be 208 kHz. Since TQ is clearly the same for D and 35Cl nuclei in the same DC1 molecule, our temperature independent ratio Tl~/Tlcl can be used to obtain (e2qQ/k)D from the microvave value [6] of (e2qQ/k)c1. We find 220 kI-Izfor (e2qQ/k)D in agreement with the theoretical value [5] and in contract with Boehme and Eisner’s 4oo/odiscrepancy [3]. If the theoretical value is correct our result shows that the quadrupole interaction in the liquid and upper solid phase is as for the free molecule. Using the microwave value for (e2qQ/h)Cl we estimate that TQ is 2.2 x lo-13 set at the melting point. This correlation time is extremely short and the question arises whether it is impossibly short on the grounds of the thermal energy and the forces available for reorientation. If the molecules are not severely restrained we may use the equipartition relation $I02 = kT for the r.m.s. angular velocity where IO is thy moment oflinertia. We expect that TQ a (32)-Z = (IO/IT)5 = = 3.5 x lo-13 set at the melting point so the ob* Supportedby an S .R .C. Research
Fellowship.
523
Volume 244,
number
10
PHYSICS
LETTERS
served value of TQ is short but not impossibly so. If the anisotropic interaction energy of the molecules is E the uncertainty principle requires that ~QE 3 A since an observable reorientation occurs in time TQ. If E is the electric dipole interaction energy of two DC1 molecules at the mean distance at the melting point we find TQ 2 lo-18 set so again the observed TQ value is possible. TIC1 for DC1 differs only slightly from TlCl for HCl. Therefore, although the moment of inertia of DC1 is virtually twice -that of HCl, the molecular reorientation time, TQ, is partically the same. This strongly suggests that the molecular reorientation is not free. Indeed, it supports the proposal [‘I] that the reorientation is by Brownian reorientational diffusion which will be discussed further in connection with proton T1 measurements in HCl [8]. Our results show that the reorientational motion of the molecules is not affected in going from the liquid to the upper phase solid. This effect has also been observed in heavy methane [9]. This result and our estimates of TQ are consistent with the observed high dielectric constant and the lack of dielectric dispersion below 10 GHz [lo]. In fact our results suggest the dielectric dispersion is centred at about 250 GHz. It seems to us likely that the molecular reorientation is also diffusional in the upper solid phzg~.
8 May 1967
Neutron scattering measurements [ll] in solid DC1 in the upper phase were found to be consistent with molecular reorientation but not for any plausible multiple site model. It would be interesting to consider the neutron scattering results for a model in which the deuterons have a probability distribution which is a spherical shell about the chlorine nuclei of radius the molecular internuclear separation, as is required by the reorientational diffusion picture.
References 1. J. G. Powles. M. Rhodes and J. H.Strange. Molecular Physics 11 (1966) 515. 2. Col~oque Ampere, XIV, Ljubljana, Sept. 1966. 3. H.Boehme and M.Eisner, Phys. Letters 24A (1967) 59. 4. E. P. Marram amd J. L.Ragle, J. Chem. Phys. 41 (1964) 3546. 5. P. E. Cade, private communication. 6. M.Coaan and W.Gordy, Phys.Rev. 11 (1958) 209. 7. K. Krynicki and J.G. Powles, Proc. Phgs.Soc. (lond.), 86 (1965) 549. 8. K. Krynicki, K. Marsden, M. Morris. J.G. Powles, M.Rhodes and J.H.Strange, Proc.Phys.Soc. (Land.) to be published. 9. M.Bloom and G.A.de Wit. Can.J.Phys. 43 (1965) 986. 10. C.S. E. Phillips, J.Phys.Rad. 13 (1952) 216. 11. E .Sandor and R. F. C. Farrow, Nature 213 (1967) 171.
*****
THE
THEORY
OF VIBRONIC
SPECTRA
IN REALISTIC
J. T. RITTER* and J. J. MARKHAM physics Department, Illinois Institute of Technology, Chicago, Received
1 April
CRYSTALS
Illinois
1967
An electron-lattice scalar interaction potential has been derived in terms of the actual lattice vibration modes and applied in the study of vibronic spectra. Good agreement is found between our calculations (lattice factor distributions) and experiments.
Many defect and impurity centers in insulators have optical vibronic spectra which display fine structure (see fig. 1). Absorption on the higher energy side of the narrow (zero-phonon) line in-
volves the creation ef phonons. Peaks in this structure arise from strong coupling of selected groups of phonons with the trapped electron. Previous theoretical studies have been primarily concerned with properties of the overall band width
* Supported by National Aeronautics
and of the zero-phonon line. Since the observed.vibronic
istration.
524
and Space Admin-
structure
has been
number
10
PHYSICS
35Cl
DEUTERONAND
SPIN
LETTERS
LATTICE
8 May 1967
RELA-XATION
IN DC1 AND
HCI
J. G. POWLES and M. RHODES* Physics Laboratories.
University of Kent! Canterbuys,
Received
England
1 April 1967
Molecular reorientation in liquid and upper solid phase DC1 is found to be rapid, and probably diffusional.
We report measurements of the nuclear spin lattice relaxation time, Tl, for deuterons in deuterium chloride in the liquid up to the critical temperature and in the higher temperature solid phase tid also the 35C1 T1 for DC1 and HCl. We used the conventional 900, T , go0 pulSe method at 9 MHz [l]. The results are shown in fig. 1 and have been briefly discussed elsewhere [ 21. They differ considerably from results recently reported for the liquid [3] by a method which is not revealed. Some preliminary measurements we have made suggest that Boehme and Eisner may have measured T2 and not Tl. We were unable to observe signals in the lower temperature solid phase. This was expected because the 35C1 pure quadrupole resonance is readily observed [4]. - 100
-150 TEMPERATURE
-50
0
%
I=
_ 100
I
I 10
I
I
6
6
4
Fig. 1. Deuteron (0, left hand ordinates in seconds) and 35c1 (0, right hanh ordinates in microseconds) s in lattice relaxation times in 90% DCl/lO% HCI. Also g5 Cl(X) relaxation times in 75% HC1/25% DCl. DBE and CBE ‘-’ are deuteron and chlorine relaxation times respectively from ref. 3. T.P. , M.P. and C.P. indicate the first order transition, melting and critical temperature respectively.
unaffected
by melting
The strongest nuclear relaxing mechanism is the electric quadrupole (eQ$ interaction with the molecular field gradient (eq) and for sufficiently rapid reorientation of the molecule l/T1 = = c(eqQ/h)2~Q where c = i for spin Z = 1, as for deuterons and c = h for Z = $, as for 35Cl nuclei. TQ is the correlation time for reorientation of the field gradient. The plots of In T1 versus -103/T, where T is the absolute temperature, are parallel straight lines which suggests that TQ has an Arrhenius temperature behaviour with an activation energy of 0.8 k&/mole (0.035 eV/molecule). Cade [5] has calculated that for DC1 (e2qQ/h)3sC1 = 67.9 MHz in agreement with the microwave value [6] 67.3 MHz. He also calculated (e2qQ/k) in DC1 to be 208 kHz. Since TQ is clearly the same for D and 35Cl nuclei in the same DC1 molecule, our temperature independent ratio Tl~/Tlcl can be used to obtain (e2qQ/k)D from the microvave value [6] of (e2qQ/k)c1. We find 220 kI-Izfor (e2qQ/k)D in agreement with the theoretical value [5] and in contract with Boehme and Eisner’s 4oo/odiscrepancy [3]. If the theoretical value is correct our result shows that the quadrupole interaction in the liquid and upper solid phase is as for the free molecule. Using the microwave value for (e2qQ/h)Cl we estimate that TQ is 2.2 x lo-13 set at the melting point. This correlation time is extremely short and the question arises whether it is impossibly short on the grounds of the thermal energy and the forces available for reorientation. If the molecules are not severely restrained we may use the equipartition relation $I02 = kT for the r.m.s. angular velocity where IO is thy moment oflinertia. We expect that TQ a (32)-Z = (IO/IT)5 = = 3.5 x lo-13 set at the melting point so the ob* Supportedby an S .R .C. Research
Fellowship.
523
Volume 244,
number
10
PHYSICS
LETTERS
served value of TQ is short but not impossibly so. If the anisotropic interaction energy of the molecules is E the uncertainty principle requires that ~QE 3 A since an observable reorientation occurs in time TQ. If E is the electric dipole interaction energy of two DC1 molecules at the mean distance at the melting point we find TQ 2 lo-18 set so again the observed TQ value is possible. TIC1 for DC1 differs only slightly from TlCl for HCl. Therefore, although the moment of inertia of DC1 is virtually twice -that of HCl, the molecular reorientation time, TQ, is partically the same. This strongly suggests that the molecular reorientation is not free. Indeed, it supports the proposal [‘I] that the reorientation is by Brownian reorientational diffusion which will be discussed further in connection with proton T1 measurements in HCl [8]. Our results show that the reorientational motion of the molecules is not affected in going from the liquid to the upper phase solid. This effect has also been observed in heavy methane [9]. This result and our estimates of TQ are consistent with the observed high dielectric constant and the lack of dielectric dispersion below 10 GHz [lo]. In fact our results suggest the dielectric dispersion is centred at about 250 GHz. It seems to us likely that the molecular reorientation is also diffusional in the upper solid phzg~.
8 May 1967
Neutron scattering measurements [ll] in solid DC1 in the upper phase were found to be consistent with molecular reorientation but not for any plausible multiple site model. It would be interesting to consider the neutron scattering results for a model in which the deuterons have a probability distribution which is a spherical shell about the chlorine nuclei of radius the molecular internuclear separation, as is required by the reorientational diffusion picture.
References 1. J. G. Powles. M. Rhodes and J. H.Strange. Molecular Physics 11 (1966) 515. 2. Col~oque Ampere, XIV, Ljubljana, Sept. 1966. 3. H.Boehme and M.Eisner, Phys. Letters 24A (1967) 59. 4. E. P. Marram amd J. L.Ragle, J. Chem. Phys. 41 (1964) 3546. 5. P. E. Cade, private communication. 6. M.Coaan and W.Gordy, Phys.Rev. 11 (1958) 209. 7. K. Krynicki and J.G. Powles, Proc. Phgs.Soc. (lond.), 86 (1965) 549. 8. K. Krynicki, K. Marsden, M. Morris. J.G. Powles, M.Rhodes and J.H.Strange, Proc.Phys.Soc. (Land.) to be published. 9. M.Bloom and G.A.de Wit. Can.J.Phys. 43 (1965) 986. 10. C.S. E. Phillips, J.Phys.Rad. 13 (1952) 216. 11. E .Sandor and R. F. C. Farrow, Nature 213 (1967) 171.
*****
THE
THEORY
OF VIBRONIC
SPECTRA
IN REALISTIC
J. T. RITTER* and J. J. MARKHAM physics Department, Illinois Institute of Technology, Chicago, Received
1 April
CRYSTALS
Illinois
1967
An electron-lattice scalar interaction potential has been derived in terms of the actual lattice vibration modes and applied in the study of vibronic spectra. Good agreement is found between our calculations (lattice factor distributions) and experiments.
Many defect and impurity centers in insulators have optical vibronic spectra which display fine structure (see fig. 1). Absorption on the higher energy side of the narrow (zero-phonon) line in-
volves the creation ef phonons. Peaks in this structure arise from strong coupling of selected groups of phonons with the trapped electron. Previous theoretical studies have been primarily concerned with properties of the overall band width
* Supported by National Aeronautics
and of the zero-phonon line. Since the observed.vibronic
istration.
524
and Space Admin-
structure
has been