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Proton spin-lattice relaxation from classical and tunneling motions of NH3 groups in Co(NH3)6Cl3
JOURNAL
OF MAGNETIC
RESONANCE
57, i23- 126 ( 1984)
NOTES Proton Spin-Lattice Relaxation from Classical and Tunneling Motions of NH3 Groups in Co(NH3)&13 J. A. J. I.OURENS Department of Physics, Rand Afriikaans University, P.O. Box 524, Johannesburg, South Africa AND
E. C. REYNHARDT Department of Physics, University of South Africa, P.O. Box 392, Pretoria, South Africa Received June 23. 1983
From measurements of the proton spin-lattice relaxation time in the rotating frame (T,,) in Co(NI-13)&13 from 77 to 400 K potential barriers and preexponential factors associated with the reorientational motions of entire Co(NI&)CI~ octahedrons were determined (I). In a powdered sample supplied by British Drug Houses the decay of the magnetization was found to be nonexponential but could be well described by the sum of two exponential functions. The results were interpreted in terms of the coexistence of two polymorphic structures (2), the nonexponentiality arising from the two noninteracting spin systems corresponding to the two structures. In a powder obtained from a single crystal grown from an aqueous solution the decay was found to be exponential, there being only one polymorphic structure in the powder. In this note we report measurements of the proton spin-lattice relaxation time in the laboratory frame (T,) from 400 to 33 K and attempt to analyze the results by considering the classical and quantum motions of inequivalent NH3 groups in the powder containing one polymorphic structure. T1 was measured at frequencies of 19, 30, and 52 MHz using the progressive saturation technique and the equipment described elsewhere (1). Temperatures were read from a calibrated platinum thermometer placed in contact with the sample. The lowest temperature that could be reached with our closed-cycle helium refrigerator was about 33 K. Figure 1 shows the measurements over the inverse temperature region 2.4 =G/3 d 30 K-’ where /3 = 1000/T. The maximum experimental error in T, was about 20%. Since the asymmetric unit of the unit cell of Co(NH3)&lJ contains 11 NH3 groups (3) we expect a number of Tl minima arising from threefold reorientations of these groups at lower temperatures. Over the region 25 G @ < 30 K-l, T, becomes independent of the Larmor frequency wo, in disagreement with the classical BPP behavior. If the relaxation results from quantum mechanical tunneling of protons within a number of equivalent NH3 groups and W, % wo, where mt is the tunneling frequency, then (4) 123
0022-2364184 $3.00 Copyright 8 1984 by Aaxlcmic Pres, Inc. All rigbhcsof reproduction in any form reserved.
124
NOTES
FIG. 1. Temperature dependence of T, at 19 MHz (A), 30 MHz (O), and 52 MHz (B). Curves A-F are discussed in the text.
l/T,=
CT/(1 + U:T2),
ill
independent of wo. The constant C contains an unknown factor representing the fractional number of tunneling NH3 groups and T = 7. exp(E/RT) where E is the energy difference between the ground and first excited torsional states. The thermal average of mt is given by (5, 6) cot = (uf - 0: exp(-E/RT))/(l
+ exp(-E/RT))
PI
where hwy and tiw: are the ground and first excited torsional state tunnel splittings. Based on experimental and theoretical values of w! for tunneling methyl groups having T, minima near B = 24 K-‘(42 K) (4, 7) we estimate L$ for NH3 groups to be approximately (2?r/3) X lo9 set-‘. Then with E = 760 cal/mol and U: also of the order of lo9 set-‘, wt = oy for inverse temperatures at least down to /3 = 15 K-’ (67 K). Curve F of Fig. 1 shows the best fit of Eq. [l] to the frequency independent data. The motional parameters are listed in Table 1. Around fl= 22 K-r (45 K), TI becomes noticeably frequency dependent, implying that classical motions of NH3 groups start contributing to the relaxation. Considering only intra-NH3 dipolar interactions, T, due to classical threefold reorientations is given by lITI
=
[31
where I = 1.68 A and ni is the number of reorienting NH3 groups involved in the formation of the ith V-shaped curve. Since the nitrogen atoms occupy only fourfold
125
NOTES TABLE
1
MOTIONALPARAMETERSASXICIATEDWITH QUANTUM MECHANICAL MOTIONS
Curveb
A B C D E F
n
E (kcal/mol)
2 4 16 16 8 -
2.8 3.2 1.7 1.4 1.1 0.76
a Curve A describes the isotropic octahedrons. b Refers to Fig. 1.
+ + + + & +
THECLASSICALAND OF NH3 GROUPS’
0.3 0.3 0.2 0.3 0.2 0.1
reorientation
7.0 4.6 8.3 7.1 8.7 6.4
x X x x X X
lo-‘* lo-l3 lo-l4 lo-l4 lo-l4 lo-l4
of two of the CO(NH3h3+
and eightfold positions (3) the values of ni are restricted to 4 and 8. The T, data at the three Larmor frequencies could be well fitted to Eqs. [l] and [3] with nl , n2, and n3 equal to 16, 16, and 8 NH3 groups, respectively. Curves C, D, and E in Fig. 1 represent these individual contributions at the frequency of 52 MHz over the relevant inverse temperature region (/3 R 9 K-‘). A best fit to the broad minimum around B = 4.5 K-’ was achieved with n4 = 4 in Eq. [3] and 2 out of 12 isotropically reorienting Co(NH3)63+ octahedrons for which (1) l/T, =
%($+S-)(l
+l#+
1 +L:,$
where r* (=3.25 A) is the distance between the centers of nearest-neighbor threespin sets within an octahedron. Dipolar interactions between nearest-neighbor octahedrons have been neglected in Eq. [4]. Curves A and B in Fig. 1 show the contributions to Tl from these two sources at 52 MHz. The solid lines in Fig. 2 represent the remarkably good fit of Eqs. [ 11, [3], and [4] to the T, data at the three Larmor frequencies from room temperature down to 33 K. The associated motional parameters are summarized in Table 1. The activation energy associated with the isotropic reorientation of the two octahedrons was taken from the TIP results (I). The 7. value of 7 X IO-l2 see obtained from the present analysis is more realistic than the value of 3 X lo-” set obtained from the TIP results. Watton et al. (8) and Armstrong et al. (9) showed that experimentally obtained T, minima associated with reorientations of ammonium groups are shallower than the calculated BPP minima if the reorientations are semiclassical. Since the activation energies of a number of NH3 groups are relatively low (between 1.1 and 1.7 kcal/ mol, cf. Table l), it is expected that tunneling influences the relaxation data to some extent. In our purely classical treatment of the data (curves C, D, and E in Fig. l), the number of NH3 groups associated with these curves could therefore have been underestimated.
126
NOTES
FIG. 2. Solid lines represent best fits of Eqs. [I], [3], and [4] at 19 MHz (A), 30 MHz (O), and 52 MHz (m). Motional parameters are given in Table 1.
At least five nonequivalent NH3 groups must be considered to explain the T, results satisfactorily. The fact that two of these nonequivalent groups consist of sixteen NH3 groups, whereas the unit cell contains only equivalent groups of four and eight NH3 groups, implies that the potentials hindering threefold reorientations of some groups are approximately the same. REFERENCES 1. E. C. RIZNHARDT, J. A. J. LOURENS, AND M. J. R. HOCH, J. Magn. Reson. 53, 76 2. E. C. REYNHARDT, J. Solid State Chem. 43, 334 (1982). 3. G. J. KRUGER AND E. C. REYNHARDT, Ada Crystallogr. Sect. B 34,915 (1978). 4. S. CLOUGH, A. HEIDEMANN, A. J. HORSEWILL, J. D. LEWIS, AND M. N. J. PALEY,
(1983). J. Phys. C 15,
2495 (1982). 5. 6. 7. 8. 9.
S. S. F. A. R.
EMID AND R. A. WIND, Chem. Phys. Mt. 33,269 (1975). CLOUGH, J. Phys. C9, L523 (1976). KOKSAL, E. RULER, AND H. SILLESCU, J. Phys. C 15, 5821 (1982). WATTON, A. R. SHARP, H. E. PETCH, AND M. M. PINTAR, Phys. Rev. B 5,4281 (1972). L. ARMSTRONG, J. A. J. LOURENS, AND K. R. JEFFREY, J. Magn. Reson. 23, 115 (1976).
OF MAGNETIC
RESONANCE
57, i23- 126 ( 1984)
NOTES Proton Spin-Lattice Relaxation from Classical and Tunneling Motions of NH3 Groups in Co(NH3)&13 J. A. J. I.OURENS Department of Physics, Rand Afriikaans University, P.O. Box 524, Johannesburg, South Africa AND
E. C. REYNHARDT Department of Physics, University of South Africa, P.O. Box 392, Pretoria, South Africa Received June 23. 1983
From measurements of the proton spin-lattice relaxation time in the rotating frame (T,,) in Co(NI-13)&13 from 77 to 400 K potential barriers and preexponential factors associated with the reorientational motions of entire Co(NI&)CI~ octahedrons were determined (I). In a powdered sample supplied by British Drug Houses the decay of the magnetization was found to be nonexponential but could be well described by the sum of two exponential functions. The results were interpreted in terms of the coexistence of two polymorphic structures (2), the nonexponentiality arising from the two noninteracting spin systems corresponding to the two structures. In a powder obtained from a single crystal grown from an aqueous solution the decay was found to be exponential, there being only one polymorphic structure in the powder. In this note we report measurements of the proton spin-lattice relaxation time in the laboratory frame (T,) from 400 to 33 K and attempt to analyze the results by considering the classical and quantum motions of inequivalent NH3 groups in the powder containing one polymorphic structure. T1 was measured at frequencies of 19, 30, and 52 MHz using the progressive saturation technique and the equipment described elsewhere (1). Temperatures were read from a calibrated platinum thermometer placed in contact with the sample. The lowest temperature that could be reached with our closed-cycle helium refrigerator was about 33 K. Figure 1 shows the measurements over the inverse temperature region 2.4 =G/3 d 30 K-’ where /3 = 1000/T. The maximum experimental error in T, was about 20%. Since the asymmetric unit of the unit cell of Co(NH3)&lJ contains 11 NH3 groups (3) we expect a number of Tl minima arising from threefold reorientations of these groups at lower temperatures. Over the region 25 G @ < 30 K-l, T, becomes independent of the Larmor frequency wo, in disagreement with the classical BPP behavior. If the relaxation results from quantum mechanical tunneling of protons within a number of equivalent NH3 groups and W, % wo, where mt is the tunneling frequency, then (4) 123
0022-2364184 $3.00 Copyright 8 1984 by Aaxlcmic Pres, Inc. All rigbhcsof reproduction in any form reserved.
124
NOTES
FIG. 1. Temperature dependence of T, at 19 MHz (A), 30 MHz (O), and 52 MHz (B). Curves A-F are discussed in the text.
l/T,=
CT/(1 + U:T2),
ill
independent of wo. The constant C contains an unknown factor representing the fractional number of tunneling NH3 groups and T = 7. exp(E/RT) where E is the energy difference between the ground and first excited torsional states. The thermal average of mt is given by (5, 6) cot = (uf - 0: exp(-E/RT))/(l
+ exp(-E/RT))
PI
where hwy and tiw: are the ground and first excited torsional state tunnel splittings. Based on experimental and theoretical values of w! for tunneling methyl groups having T, minima near B = 24 K-‘(42 K) (4, 7) we estimate L$ for NH3 groups to be approximately (2?r/3) X lo9 set-‘. Then with E = 760 cal/mol and U: also of the order of lo9 set-‘, wt = oy for inverse temperatures at least down to /3 = 15 K-’ (67 K). Curve F of Fig. 1 shows the best fit of Eq. [l] to the frequency independent data. The motional parameters are listed in Table 1. Around fl= 22 K-r (45 K), TI becomes noticeably frequency dependent, implying that classical motions of NH3 groups start contributing to the relaxation. Considering only intra-NH3 dipolar interactions, T, due to classical threefold reorientations is given by lITI
=
[31
where I = 1.68 A and ni is the number of reorienting NH3 groups involved in the formation of the ith V-shaped curve. Since the nitrogen atoms occupy only fourfold
125
NOTES TABLE
1
MOTIONALPARAMETERSASXICIATEDWITH QUANTUM MECHANICAL MOTIONS
Curveb
A B C D E F
n
E (kcal/mol)
2 4 16 16 8 -
2.8 3.2 1.7 1.4 1.1 0.76
a Curve A describes the isotropic octahedrons. b Refers to Fig. 1.
+ + + + & +
THECLASSICALAND OF NH3 GROUPS’
0.3 0.3 0.2 0.3 0.2 0.1
reorientation
7.0 4.6 8.3 7.1 8.7 6.4
x X x x X X
lo-‘* lo-l3 lo-l4 lo-l4 lo-l4 lo-l4
of two of the CO(NH3h3+
and eightfold positions (3) the values of ni are restricted to 4 and 8. The T, data at the three Larmor frequencies could be well fitted to Eqs. [l] and [3] with nl , n2, and n3 equal to 16, 16, and 8 NH3 groups, respectively. Curves C, D, and E in Fig. 1 represent these individual contributions at the frequency of 52 MHz over the relevant inverse temperature region (/3 R 9 K-‘). A best fit to the broad minimum around B = 4.5 K-’ was achieved with n4 = 4 in Eq. [3] and 2 out of 12 isotropically reorienting Co(NH3)63+ octahedrons for which (1) l/T, =
%($+S-)(l
+l#+
1 +L:,$
where r* (=3.25 A) is the distance between the centers of nearest-neighbor threespin sets within an octahedron. Dipolar interactions between nearest-neighbor octahedrons have been neglected in Eq. [4]. Curves A and B in Fig. 1 show the contributions to Tl from these two sources at 52 MHz. The solid lines in Fig. 2 represent the remarkably good fit of Eqs. [ 11, [3], and [4] to the T, data at the three Larmor frequencies from room temperature down to 33 K. The associated motional parameters are summarized in Table 1. The activation energy associated with the isotropic reorientation of the two octahedrons was taken from the TIP results (I). The 7. value of 7 X IO-l2 see obtained from the present analysis is more realistic than the value of 3 X lo-” set obtained from the TIP results. Watton et al. (8) and Armstrong et al. (9) showed that experimentally obtained T, minima associated with reorientations of ammonium groups are shallower than the calculated BPP minima if the reorientations are semiclassical. Since the activation energies of a number of NH3 groups are relatively low (between 1.1 and 1.7 kcal/ mol, cf. Table l), it is expected that tunneling influences the relaxation data to some extent. In our purely classical treatment of the data (curves C, D, and E in Fig. l), the number of NH3 groups associated with these curves could therefore have been underestimated.
126
NOTES
FIG. 2. Solid lines represent best fits of Eqs. [I], [3], and [4] at 19 MHz (A), 30 MHz (O), and 52 MHz (m). Motional parameters are given in Table 1.
At least five nonequivalent NH3 groups must be considered to explain the T, results satisfactorily. The fact that two of these nonequivalent groups consist of sixteen NH3 groups, whereas the unit cell contains only equivalent groups of four and eight NH3 groups, implies that the potentials hindering threefold reorientations of some groups are approximately the same. REFERENCES 1. E. C. RIZNHARDT, J. A. J. LOURENS, AND M. J. R. HOCH, J. Magn. Reson. 53, 76 2. E. C. REYNHARDT, J. Solid State Chem. 43, 334 (1982). 3. G. J. KRUGER AND E. C. REYNHARDT, Ada Crystallogr. Sect. B 34,915 (1978). 4. S. CLOUGH, A. HEIDEMANN, A. J. HORSEWILL, J. D. LEWIS, AND M. N. J. PALEY,
(1983). J. Phys. C 15,
2495 (1982). 5. 6. 7. 8. 9.
S. S. F. A. R.
EMID AND R. A. WIND, Chem. Phys. Mt. 33,269 (1975). CLOUGH, J. Phys. C9, L523 (1976). KOKSAL, E. RULER, AND H. SILLESCU, J. Phys. C 15, 5821 (1982). WATTON, A. R. SHARP, H. E. PETCH, AND M. M. PINTAR, Phys. Rev. B 5,4281 (1972). L. ARMSTRONG, J. A. J. LOURENS, AND K. R. JEFFREY, J. Magn. Reson. 23, 115 (1976).