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Spin-lattice relaxation of nuclear dipolar energy in (NH4)2PbCl6
Volume 54A, number 2
PHYSICS LE1TERS
25 August 1975
SPIN-LATTICE RELAXATION OF NUCLEAR DIPOLAR ENERGY IN (NH4 )2 PbCI6 M. PUNKKJNEN, J.E. TUOHI and E.E. YLINEN Wihun Physical Laboratory, University of Turku, SF-20500 Turku .50, Finland Received 30 June 1975 Experiments on the spin-lattice relaxation of nuclear dipolar energy in (NH4)2PbC16 in the temperature range 4.2 to 90 K suggest that the 120°and 180°reorientations of a tunnelling ammonium ion may take place at distinctly different rates.
Nuclear magnetic resonance studies on the proton Zeeman relaxation m polyciystalhne (NH4)2 PbCl6 show that the ammonium ion tunnelling splitting hvF between the F and A species torsional levels varies from VF =47.6 MHz at 4.2 Kto VF = 12.5 MHz at 50.6 K [1,2] ,where F refers to the 3-dimensional and A to the identical representation theof tetrahedral group. irreducible The spin-lattice relaxationof time protons, T 1, measured at the proton resonance frequency 9.0 MHz, is about 1 sat 20 K [1] When the tunnelling splitting is larger than the Zeeman splitting hv0, the relaxation is slowed down as described before [3]. Eq. (11) in ref. [3] yields an effective correlation
lOG
T,D(ms)
10 000
00 0
0o~,~
00
g
~O
0
T (K)
.
time of about 4 ps at 20 K depending on the relative magnitude of r and r’, which are the respective correlation times of the F and E type operators of the dipolar interaction [3,4]. The free induction decay (fid) shape is observed to change at about 30 K. The lengthening of fid with increasing temperature usually means that the correlation time becomes shorter than the spin-spin relaxation time T2 [5]. In the case of (14)2 PbCl6 this means that one type of motion should have a correlation time longer than 100 ps below 30 K, a considerably longer value than 4 ps obtamed from the T1understanding measurements.of the motions we To get a better studied the spm-lattace relaxation time T 1D of the dipolar energy in polycrystalline (NH4)2PbC16. The experiments were carried out at the proton resonance frequency 23.8 MHz with the Bruker SXP 4-60 pulsed NMR spectrometer. We used the pulse sequence 90° 0 0 —t1 —45~o —t—4590o [6],wheret1 was40Ms and t the time during which the relaxation took place. The relaxation appeared to be remarkably nonexponential at 4.2 K. The degree of nonexponentiality de-
0.10
~
30
40
60
00
70
00
00
100
~Fig.1. SpIn-latticerelaxationiime of the dipolar energy, T1D, in polycrystalline (NH4)2PbCl6 as a function of temperatures.
creasedwith increasing temperature until at 60 K an exponential relaxation was observed. The results shown in fig. 1 were obtained from the initial slope of the dipolar signal amplitude versus time curve. The density matrix method can be used to evaluate T1D above the line-width transition temperature [7]. When the dipolar energy consists of the interaction between the protons in neighbouring ammonium ions and the relaxation is caused by the intra-amrnonium interaction,4fl2 we obtain [8] r 1 = 3 ~ 6fr + 6(1 2/) —
—
—
—
T1D 16 r6
1+c~,2r2 o
+ 6(1
+/)
2 2 + (I
—
3/’~’
(1)
I + 4~0r +6f
____
2 ,230fl
T
2 ‘2
1+ 1 + 4(~~0r Here r is the intra-ammonium proton-proton distance, 4O ~ sin~Ocos 4 0, and 0 and 0 are —
f sin~O ~sin —
133
Volume 54A, number 2
PHYSICS LETTERS
the polar angles of the magnetic field in the coordinate system defined by the cube with the ammonium protons at its four apices. The correlation times r and T are related to the reorientation rates k2 and k3 of the ammonium ion about its 2-fold and 3-fold axes, respectively, by the equations [3] k~+k —
=
3
=
~ k3.
(2)
Eq. (1) should be applicable to (NH4)2PbC16 as far as the tunnelling effects can be ignored. For the magnetic field orientation (100) it yields the minimum value 1.8 ms at w0r I with the proton resonance frequency 23.8 MHz. However, no minimum near w0r 1 is expected for the orientations (110) and (111) or with a powder sample. The magnitude 4.5 ms of the experimentally observed minimum at 70 K as well as its distinctness lend further evidence for the presence of tunnelling effects below 70 K. The other minimum around 30 K occurs at the ternperature where the fid shape changes. Therefore, the method of slow motion [9] should be applicable to the evaluation of T1D below 30 K. However, one type of motion is probably slow and the other fast in the time scale of the fid measurements. Such an argument is supported by the fact that the proton second mo2 below 20 K. This is much ment M2 is about 6 gauss smaller than the value 16 to 20 gauss2 predicted in the case of slow motions (both types) and large tunneffing splittings [4,10]. As the E type term of the secular dipolar interaction is affected only by the 120°reorientations and the F type term by both the 120°and 180° reorientations, it seems probable that the rate k 3 is slow below 30 K and k2 fast. If we assume that the dipolar energy consists of the E type secular intra-ammomum dipolar interaction and that its relaxation is caused by 120°reorientations at average intervals of r’, we obtain the simple expression [9] 1 — 1 ——--r=~k3. T1D ‘~
(3)
The experimental result T1D = 1.3 ms at 20K yields = 1.3 ms, which is more than two orders of magnitude larger than the value 4 ps deduced from the T1 data. The 1800 reorientations should also relax the dipolar energy. If the dipolar energy consists of the E type secular interaction as above and the relaxation is caused by the fast time variation of the F type secular 134
interaction (w0
25 August 1975
hr ~ ~w, where z~wis the linewidth), the density matrix method yields the contribution 1 3 74~2 (4) ~
for a polycrystalline sample. For r = 1 ps eq. (4) gives T1D 1 ms, which is of the same magnitude as the experimental result at 20 K. At lower temperatures T1D is observed to increase in agreement with eq. (3) but in disagreement with eq. (4). If the present interpretation is correct, the effectiveness of the 180°reorientations seems to be exaggerated by eq. (4). In any case, the presence of a term proportional to (4) would predict another minimum in T1D and another change in the fid shape below 4.2 K at z~wr 1. The experimental accuracy was not good enough to decide, if the equality of the T1D values at the temperatures 4.2 K and 6.8 K is indicative of such a transition. So we suggest that the Zeeman relaxation is dominated by the 180°reorientations below 60 K and the relaxation of the dipolar energy is determined by the 120°reorientationsin the temperature range 60 to 4.2 K. If the assumption of the different magnitudes of the 120°and 180°reorientation rates proves to be right, it may help to solve the long-lived problem in the NMR of samples containing fast tunnelling tetrahedral four proton groups. In such samples the proton fid does not change at the temperature expected on the basis of correlation times deduced from the Zeeman relaxation data [10].
[1] i.E. Tuohi, E.E. Ylinen and L.K.E. Niemelä, Proc. 18th Ampere Congress, eds. P.S. Allen, E.R. Andrew and C.A. Bates (Nottingham, 1974), p. 399. [2] M. Punkkinen, J.E. Tuohi and E.E. Ylinen, to be published. [3] M. Punkkinen, i. Magn. Reson., in the press. [4] A. Watton and H.H. Petch, Phys. Rev. B7 (1973) 12. [5] D.E. Barnaal and I.J. Lowe, 1. Chem. Phys. 48 (1968) 4614. [6] J. Jeener, R. DuBois and P. Broekaert, Phys. Rev. 139 (1965) A1959. [7) J. Jeener, in Advances in magnetic resonance, Vol. 3, ed. J.S. Waugh (Academic Press, New York, 1968). [8] M. Punkkinen, Proc. XVII Congress AMPERE, ed. V. Hovi (North Holland Publishing Co., Amsterdam, 1973), p. 219. [9] C.P. Slichter and D.C. Ailion, Phys. Rev. 135 (1964) [10] A1099. A. Watton, A.R. Sharp, H.E. Peth and M.M. Pintar, Phys. Rev. B5 (1972) 4281.
PHYSICS LE1TERS
25 August 1975
SPIN-LATTICE RELAXATION OF NUCLEAR DIPOLAR ENERGY IN (NH4 )2 PbCI6 M. PUNKKJNEN, J.E. TUOHI and E.E. YLINEN Wihun Physical Laboratory, University of Turku, SF-20500 Turku .50, Finland Received 30 June 1975 Experiments on the spin-lattice relaxation of nuclear dipolar energy in (NH4)2PbC16 in the temperature range 4.2 to 90 K suggest that the 120°and 180°reorientations of a tunnelling ammonium ion may take place at distinctly different rates.
Nuclear magnetic resonance studies on the proton Zeeman relaxation m polyciystalhne (NH4)2 PbCl6 show that the ammonium ion tunnelling splitting hvF between the F and A species torsional levels varies from VF =47.6 MHz at 4.2 Kto VF = 12.5 MHz at 50.6 K [1,2] ,where F refers to the 3-dimensional and A to the identical representation theof tetrahedral group. irreducible The spin-lattice relaxationof time protons, T 1, measured at the proton resonance frequency 9.0 MHz, is about 1 sat 20 K [1] When the tunnelling splitting is larger than the Zeeman splitting hv0, the relaxation is slowed down as described before [3]. Eq. (11) in ref. [3] yields an effective correlation
lOG
T,D(ms)
10 000
00 0
0o~,~
00
g
~O
0
T (K)
.
time of about 4 ps at 20 K depending on the relative magnitude of r and r’, which are the respective correlation times of the F and E type operators of the dipolar interaction [3,4]. The free induction decay (fid) shape is observed to change at about 30 K. The lengthening of fid with increasing temperature usually means that the correlation time becomes shorter than the spin-spin relaxation time T2 [5]. In the case of (14)2 PbCl6 this means that one type of motion should have a correlation time longer than 100 ps below 30 K, a considerably longer value than 4 ps obtamed from the T1understanding measurements.of the motions we To get a better studied the spm-lattace relaxation time T 1D of the dipolar energy in polycrystalline (NH4)2PbC16. The experiments were carried out at the proton resonance frequency 23.8 MHz with the Bruker SXP 4-60 pulsed NMR spectrometer. We used the pulse sequence 90° 0 0 —t1 —45~o —t—4590o [6],wheret1 was40Ms and t the time during which the relaxation took place. The relaxation appeared to be remarkably nonexponential at 4.2 K. The degree of nonexponentiality de-
0.10
~
30
40
60
00
70
00
00
100
~Fig.1. SpIn-latticerelaxationiime of the dipolar energy, T1D, in polycrystalline (NH4)2PbCl6 as a function of temperatures.
creasedwith increasing temperature until at 60 K an exponential relaxation was observed. The results shown in fig. 1 were obtained from the initial slope of the dipolar signal amplitude versus time curve. The density matrix method can be used to evaluate T1D above the line-width transition temperature [7]. When the dipolar energy consists of the interaction between the protons in neighbouring ammonium ions and the relaxation is caused by the intra-amrnonium interaction,4fl2 we obtain [8] r 1 = 3 ~ 6fr + 6(1 2/) —
—
—
—
T1D 16 r6
1+c~,2r2 o
+ 6(1
+/)
2 2 + (I
—
3/’~’
(1)
I + 4~0r +6f
____
2 ,230fl
T
2 ‘2
1+ 1 + 4(~~0r Here r is the intra-ammonium proton-proton distance, 4O ~ sin~Ocos 4 0, and 0 and 0 are —
f sin~O ~sin —
133
Volume 54A, number 2
PHYSICS LETTERS
the polar angles of the magnetic field in the coordinate system defined by the cube with the ammonium protons at its four apices. The correlation times r and T are related to the reorientation rates k2 and k3 of the ammonium ion about its 2-fold and 3-fold axes, respectively, by the equations [3] k~+k —
=
3
=
~ k3.
(2)
Eq. (1) should be applicable to (NH4)2PbC16 as far as the tunnelling effects can be ignored. For the magnetic field orientation (100) it yields the minimum value 1.8 ms at w0r I with the proton resonance frequency 23.8 MHz. However, no minimum near w0r 1 is expected for the orientations (110) and (111) or with a powder sample. The magnitude 4.5 ms of the experimentally observed minimum at 70 K as well as its distinctness lend further evidence for the presence of tunnelling effects below 70 K. The other minimum around 30 K occurs at the ternperature where the fid shape changes. Therefore, the method of slow motion [9] should be applicable to the evaluation of T1D below 30 K. However, one type of motion is probably slow and the other fast in the time scale of the fid measurements. Such an argument is supported by the fact that the proton second mo2 below 20 K. This is much ment M2 is about 6 gauss smaller than the value 16 to 20 gauss2 predicted in the case of slow motions (both types) and large tunneffing splittings [4,10]. As the E type term of the secular dipolar interaction is affected only by the 120°reorientations and the F type term by both the 120°and 180° reorientations, it seems probable that the rate k 3 is slow below 30 K and k2 fast. If we assume that the dipolar energy consists of the E type secular intra-ammomum dipolar interaction and that its relaxation is caused by 120°reorientations at average intervals of r’, we obtain the simple expression [9] 1 — 1 ——--r=~k3. T1D ‘~
(3)
The experimental result T1D = 1.3 ms at 20K yields = 1.3 ms, which is more than two orders of magnitude larger than the value 4 ps deduced from the T1 data. The 1800 reorientations should also relax the dipolar energy. If the dipolar energy consists of the E type secular interaction as above and the relaxation is caused by the fast time variation of the F type secular 134
interaction (w0
25 August 1975
hr ~ ~w, where z~wis the linewidth), the density matrix method yields the contribution 1 3 74~2 (4) ~
for a polycrystalline sample. For r = 1 ps eq. (4) gives T1D 1 ms, which is of the same magnitude as the experimental result at 20 K. At lower temperatures T1D is observed to increase in agreement with eq. (3) but in disagreement with eq. (4). If the present interpretation is correct, the effectiveness of the 180°reorientations seems to be exaggerated by eq. (4). In any case, the presence of a term proportional to (4) would predict another minimum in T1D and another change in the fid shape below 4.2 K at z~wr 1. The experimental accuracy was not good enough to decide, if the equality of the T1D values at the temperatures 4.2 K and 6.8 K is indicative of such a transition. So we suggest that the Zeeman relaxation is dominated by the 180°reorientations below 60 K and the relaxation of the dipolar energy is determined by the 120°reorientationsin the temperature range 60 to 4.2 K. If the assumption of the different magnitudes of the 120°and 180°reorientation rates proves to be right, it may help to solve the long-lived problem in the NMR of samples containing fast tunnelling tetrahedral four proton groups. In such samples the proton fid does not change at the temperature expected on the basis of correlation times deduced from the Zeeman relaxation data [10].
[1] i.E. Tuohi, E.E. Ylinen and L.K.E. Niemelä, Proc. 18th Ampere Congress, eds. P.S. Allen, E.R. Andrew and C.A. Bates (Nottingham, 1974), p. 399. [2] M. Punkkinen, J.E. Tuohi and E.E. Ylinen, to be published. [3] M. Punkkinen, i. Magn. Reson., in the press. [4] A. Watton and H.H. Petch, Phys. Rev. B7 (1973) 12. [5] D.E. Barnaal and I.J. Lowe, 1. Chem. Phys. 48 (1968) 4614. [6] J. Jeener, R. DuBois and P. Broekaert, Phys. Rev. 139 (1965) A1959. [7) J. Jeener, in Advances in magnetic resonance, Vol. 3, ed. J.S. Waugh (Academic Press, New York, 1968). [8] M. Punkkinen, Proc. XVII Congress AMPERE, ed. V. Hovi (North Holland Publishing Co., Amsterdam, 1973), p. 219. [9] C.P. Slichter and D.C. Ailion, Phys. Rev. 135 (1964) [10] A1099. A. Watton, A.R. Sharp, H.E. Peth and M.M. Pintar, Phys. Rev. B5 (1972) 4281.