NMR LINE SHAPE AND CROSS RELAXATION OF ... - Science Direct

Volume 161, number 6

CHEMICAL PHYSICS LETTERS

29 September 1989

NMR LINE SHAPE AND CROSS RELAXATION OF TUNNELING AMMONIUM PROTONS IN (NH&Zm% A.H. WORE&U,

M. PUNKKINEN and E.E. YLINEN

WihuriPhysicalLaboratov and Departmentof PhysicalSciences, Universityof Turku,SF-20500 Turku,Finland Received 6 June 1989

The second moment M2 of the proton NMR spectrum and the time constant Tso of the magnetization transfer between the protons of the A and T symmetry species of NH: ions were measured as functions of crystal orientation and temperature down to 4.5 K in (NH,),ZnCL,. A& increases in two stepswith decreasing temperature and shows, between the steps, a strong dependence on orientation. T,, has a maximum of 3 ms at 12 K. The Tsodataand earlier results on T,r,, the spin-lattice relaxation time of the dipolar energy, are compared with a model. The results are explained by the presence of two kinds of ammonium sites in this compound.

1. Introdoctlon (NH&Z&l., has been extensively studied by different methods because of the ferroelectricity and incommensurability lt exhibits in some of its many phases [ I-71. Recently we measured the spin-lattice relaxation time of the Zeeman and dipolar energy, T, and T, D,of protons in a single crystal of this compound and found several tunnel splittings by NMR level crossing [ 8 1. If the potential hindering the reorientations of the NH: ion is weak, the proton tunneling splits the twelvefolddegenerate rotational ground state of the tetrahedral ion into levels with A, T, Ea and Eb symmetry. The A level is non-degenerate and the E levels have equal energies, but the ninefold degenerate T level further splits if the symmetry of the NH: site is lower than tetrahedral [ 91. Symmetry considerations relate the total nuclear spin of 2, 1 or 0 to the protons in an A, T or E species ion, respectively [ 101. In a level-crossing experiment T, is measured in the slow-motion region as a function of the Zeeman field B. or of the resonance frequency vo=yBo/2a. When the splittings A++T, A*E or T*T’ are equal to hv, or 2h vo, minima are observed in T, [ 111. The prominent level-crossing frequencies found in (NH&ZnCl, are explained by the level scheme AT-ZT-E (in ascending order) with separations of

24.5, 13 and 14 MHz at 20 K [ 81. Such a scheme is produced for example by a trigonal distortion malcing tunneling prefercd about one of the four threefold axes [ 91. According to X-ray studies there are 24 ammonium ions in the unit cell below 270 K [ 5 1. The number of nearest-neighbour chlorine atoms to an ammonium ion in the low-temperature phase is either 5 or 8 leading to at least two non-equivalent ammonium sites [ 61. We label the ions with the above-mentioned level structure by I and the others by II although we do not know to which sites each of them belongs. Besides the r, minima related to type I ions in the studied frequency range 5-60 MHz, an unpaired shallow minimum was observed at 32.7 MHz which could be related to type II ions. The level-crossing minima in T, corresponding to the tunnel splitting T++2T were observed to divide into two above 20 R with the higher-frequency branch broadening beyond observation around 27 K [ 8 1. This phenomenon was attributed to the splitting of the 2T level although no branching was observed in the splitting A*2T. The broadening was explained by the “quickening” of one of the ammonium motions. The remaining minima broaden below 50 K The presence of at least two motions is consistent with the appearance of two minima and a shoulder in the curve of ri, versus temperature, at 36,2 1 and 14 K, respectively. Also the blunt shape

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of the reorientation-related T, minimum could arise from several unresolved minima. Whether the motions should be attributed to non-equivalent ions or to non-equivalent rotation axes of equivalent ions, was not clear. To solve these problems we examined in the present study the proton resonance spectrum as functions of temperature and crystal orientation. The sensitivity of the experimentally measured second moment Mz to molecular motions makes it a useful parameter in line shape analysis. The intra-ion contribution to Mz from the ammonium protons is averaged to zero by fast isotropic reorientation, while large tunnel splittings decrease M2 substantially [ lo,12 1. In section 3 we compare our experiments with calculations [ 13-151 to gain more insight into the ammonium motions in (NH,,)&Q. The main purpose of the present study was to continue our investigations into proton spin diffusion and cross relaxation in ammonium compounds [ 16181. Therefore we measured TsD, the time constant of the magnetization transfer between the A and T species, in (NH,),ZnCl,. The protons of ammonium ions with different symmetries can have different spin temperatures at low temperatures. In the slow-motion region the intra-dipolar interaction makes the Zeeman energy levels of the T symmetry ions slightly non-equidistant [ lo,12 1. This delays the spin diffusion, especially between species separated by the tunnel splittings. The magnetization transfer, however, also takes place via cross relaxation involving some energy exchange between the spins and the lattice [ 181. The rate of this transfer can be measured by the Goldman-Shen pulse sequence [ 16,191. Our results for the present compound are discussed in section 4.

by a liquid helium bath. It could be rotated about the crystalline Q axis perpendicular to the static magnetic field &_ In the figures of this paper p= 7’ corresponds to the orientationB& and o= 97” to Bolla. All the experiments were carried out using a Bruker SXP 4-100 spectrometer at 37.0 MHz near one of the level crossing frequencies giving a small value for T,. Even then T, was as long as 150 s at the lowest temperature.

3. Second moment The temperature dependence of the proton Mz for B,, roughly parallel to the crystalline c axis is shown in fig. 1. The values measured at the two lowest temperatures should be treated with caution because the spectral window of 100 kHz was a bit too narrow for those spectra. Fig. 2 shows the orientation dependence of M2 at three temperatures. In addition, M2 was measured at 79 K where the entire intra-ion contribution is averaged to zero. The inter-ion value varies between 0.018 and 0.022 mT2 depending on the orientation. M2 increases in two stages with decreasing temperature: around 35 K to 0.03-0.07 mT* (orientation dependence) and again below 20 IC to at least 0.15 mT*. The stepwise growth is in accordance with the two ED minima observed before [ 8 1. The large anisotropy between 35 and 20 IS has de-

a.5

K

10K 43 K

2. Sample and apparatns A single crystal of (NH4)2ZnC14 weighing 0.54 g was grown by slow evaporation at 35°C from an aqueous solution of NH&l and ZnClz in the molar ratio 2: 1. This sample had already been used in our earlier T, measurements [ 81. The orientation of the crystal was determined by comparing the angles between the growth faces to the structure given in ref. [ 5 1. The sample was sealed in the probe and cooled 562

kHz -

cl00 .

l

m .

‘*.

1

1

I

IO

20

I

1

40

30 Temperature

..

.

1

50

(K)

Fig. I, Proton M2 versus temperaturefor pr=O”or roughly41~ (mT”= 100G*).

*... .1.

CHEMICAL PHYSICS LETTERS

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-

;

0.15

5 i E

a

0.10

t

. .

.

.

l

I

n

. ,.

E

.

s ii

”

0.05

.

450

.

l

.

0’

.

.’

0.

go0

Angle

135”

1500

q~

-50

0 Frequency

50 (kHd

Fig. 2. Proton Ms versus the orientation of Bs in the crystalline acplaneat4.5(A),lO(~)and20K(O).Thecorresponding spectra at 20 K arc also shown.

to some extent at 10 K and cannot be observed at 4.5 K. In the interpretation of our data we use theoretical M2 (intra)-values computed for NH: powder samples [ 141 and, in some cases, for single crystals [ 13,151. To make the comparison easier we summarize the relevant information in table 1. The orientation-dependent values do not include the small nitrogen contribution. In our case A4,=M2 (inter)+~Mz(I)+&Vz(II), where I and II refer to the ions at the two non-equivalent sites. The level structure A-T-2T-E of type I creased

29 September 1989

ions denotes the powder average value of &(I) =0.09 mT2 below the line-width transition temperature. This leads together with the measured values to M2(II)>2(0.15-0.02-fx0.09) mT2= 0.17 mT2, which exceeds slightly the value for tetrahedral symmetry A-3T-E, is clearly larger than the value expected in the presence of more than two large splittings and falls considerably below the value for no tunneling. Tunneling about twofold axes is usually believed to be much slower than about threefold axes. Under these conditions one is left, besides the poorly fitting ahemative of tetrahedral symmetry, with the scheme A + T-2T + E corresponding to tunneling about one trigonal axis only. The ions with smalI splittings should be strongly hindered and their motion should slow down at high temperature. The first step in M2, about 0.03 mT2, could be produced by the slowing down of either (a) type I ions with the level structure A-T-T-T-E (the 2T level is probably split above 20 K) or (b) the motion about the slower threefold axes of type II ions with the level structure A+T-2T+E. Both altematives give an angular dependence of the right magnitude. The sharpness of most of the level-crossing T1 minima up to 40 K suggests that the type I ions are slowing down first which supports case (a). The bigger step below 20 K arises mainly from additional slowing down of the motions and, to a smaller extent, from the change in the level structure of type I ions, from A-T-T-T-E to A-T-ZT-E with decreasing temperature. The alternative to (a) would

Table 1 The theoretical second moment I%&(intra) of ammonium protons [ 13- 151(in mT2 = 100 @ ). The hyphen denotes a large splitting and the symbols 2f or 2f mean fast tunneling exclusively about the two- or threefolds axes, respectively. Reorientation

Tunnel splittings

Powder average

Orientation dependence

none none none none none none none none none none one fast axis

none A+E+T-2T (2f) A+E-3T (2f) A+T-2T+E (3f) A+E-T-2T (2f) A-E-3T A-3T-E (3f) A-E-T-2T A-T-ZT-E ( 3f) A-T-T-T-E large

0.511 0.261 0.221 0.185 0.162 O.lS7 0.155 0.098 0.091 0.061 0.032

0.29-0.58 anisotmpic isotropic 0.05-0.58 anisotropic isotropic isotropic anisotropic 0.05-0.15 O-O.15 O-0.08

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mean the total slowing down of type II ions, but in case (b) the motions of the type I ions and the remaining motion of the type II ions about their fast axis would slow down practically simultaneously below 20 K. The disappearance of the angular dependence could result from the different orientations of the ions. Case (b) would require that the type II ions are identically oriented in the unit cell, but then their level structure At T-2T t E should give rise to an observable anisotropy in MZ even at the lowest temperature. To obtain an orientation-independent M2 at 4.5 K in case (a) would require the preferred threefold axis of the type II ions to be oriented in such a way that the anisotropy originating from the type I ions is cancelled. The level structure A-3T-E of type II ions cannot result in such a cancellation. The presence of several motions could also appear in the shape of the reorientation-related T, minimum above 50 K [ 81. A rather good fit was obtained by assuming that half of the ions reorientate preferably about one threefold axis [ 201, but the presence of non-zero tunnel splittings prevents any definite conclusions.

29 September 1989

I 0.2

cc P

d

0.1

1, : 200 Ins 10 ms 1 ms

0.0 0

0.1 Ills

. I 0

1

I

I

I

5

10

15

20

Time

t2 (ma)

Fig. 3. Ratio R of the wings to the total area of the spectrum from the pulse sequence 900,-16 ~~s-900_,-t~-90”at 12.5 K for p=O” and the fitted curve R(12)=0.257-0.086exp( -tJOS ms) - 0.20 I exp ( - CJ5ms). Spectra for some values of f, are also shown.

4.00~~ relaxation The cross-relaxation time T,, was measured by the Goldman-Shen pulse sequence 90;-t,-9O?,t,90” [ 191. It is applicable in the case of ammonium protons below the line-width transition temperature due to intradipolar shifts of the T species levels [ 161. The fixed interval t, is adjusted to dephase maximally the wings of the spectrum or the T ,species magnetization. Thus the magnetization after the second 90” pulse originates mostly from the A species ions. The shape of the spectrum after the third pulse indicates how much magnetization transfer has taken place during the variable time tz. Fig. 3 shows one such series of experiments. The parameter R measured as a function of t2 is the ratio of the wings to the whole spectral area. In (NH,),ZnCl., the magnetization transfer or cross relaxation was usually non-exponential. Therefore we fitted the five-parameter function R(t2)=Rm-Aexp( -tz/TA)Bexp ( - tl/TB) to the experimental ratios and de-

564

10

20 Temwrature

30 (K)

00 900 Angle 0

Fig, 4. (a) Tso (e) for B,Jc and TID (0) for B,# versus temperature. (b) T, versus the orientation of BOin the UCplane at 10K (m) and20K(O).

fined T,, to be the time during which [R, - R ( tz ) ] / (A t B) decreased to 1/e. In fig. 4a we plot the temperature dependence of T,, for B,, approximately parallel to the crystalline c axis and, for comparison, some of our earlier T,, results for B&5 [ 8 1. T,, has a maximum at 12 K and becomes clearly shorter than T,, at the lowest temperatures. Fig. 4b shows that the orientation dependence of T,, is more prominent at 10 K than at 20 K. In addition, TsD reaches its relative maximum at the same orientations at M2. The orientation de-

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pendence of T,, at such low temperatures has not been measured. In all ammonium compounds studied so far TsD increases monotonically with decreasing temperature [ 16- 181. This is in accordance with the model derived for cross relaxation [ 181. If the dominant transitions are time-dependent, their rate in the slowmotion regime is proportional to the rate of the motion or TSDu~, the correlation time of the NH1 reorientations. The maximum in T,, can be understood by the presence of two non-equivalent ions in ( NH4) rZnCll. Above the line-width transition temperature of the faster ions only the magnetization of the slower ions is reduced by the pulse sequence and thus TsDu r (slow). When with decreasing temperature t(fast) also exceeds the inverse line width, TsDoc1/ [ l/ r(slow)+l/r(fast)]~r(fast).ThemaximumofT, appears at the temperature where the increasing contribution of the faster ions overcomes the lengthening of r( slow). Such an explanation is supported by the fact that above 15 K the cross relaxation is almost exponential but at lower temperatures clearly non-exponential (see fig. 3 ). According to the calculations TsD< T,, in the slowmotion region if the T levels are nondegenerate but TsD> T,, if at least two of them remain degenerate [ 181. In (NH4)2ZnC14 at the lowest temperatures T,, is much smaller than TID, the time constants being mainly determined by the faster ions. This would require the total lifting of the T 1eveI degeneracy. Therefore type I ions, having the level structure A-T-ZT-E, cannot be the faster ones. For the type II ions our Mz results suggest at least partly degenerate T levels. Nevertheless, it may be possible that the level structure A + T-2T + E would agree with our experimental results. In this case the A and one of the T levels are mixed by the time-independent intra-dipolar interaction, but the model in ref. [ 18 ] as well as our interpretation for the effect of the threepulse sequence presumes no mixing. The relaxation of the dipolar energy, on the other hand, necessarily requires energy exchange with the lattice. Therefore T, Dis proportional to the correlation time of the motion in this case also and is thus longer than T,,. If the model [ 181 for the T,, and T,, processes is valid and the line-width transition temperature of the type I ions is high enough, the proposed lifting

29 September 1989

of the degeneracy of the 2T levels should make T,D greater than TsD at temperatures above 20 K. In fig. 4a this is indeed seen to occur. This explanation supports case (a) in section 3. The change in the hindering potential which splits the 2T levels could also give rise to the fast motion which broadens two of the level-crossing minima in T, around 27 K. The TsD measurements in tunneling ammonium compounds were initially recorded to test the proposal that the non-exponentiality of the proton T1 relaxation observed at low temperatures is caused by different relaxation rates of the A and T magnetizations due to slow spin diffusion between them [ 2 11. In addition to (NH,),ZnCl, we have earlier studied T,, in (NH,)$nBr, [ 161, NI-I&104 [ 171 and ( NH4 ) ,PbCl, [ 18 1. In all these compounds TsD is several orders of magnitude shorter than T, contradicting that proposal. For the source of the nonexponentiality we instead proposed a distribution of tunnel splittings [ 171. It has also been proposed that, if the A and T levels are separated by tunneling, no adiabatic transfer of magnetization can occur between them [ 211. Consideration of the time-independent symmetryconserving inter-dipolar flip-flop transitions shows, analogously to the case of the methyl group [ 22 ] , that an adiabatic process is possible and places an upper limit of the order of 100 ms to the lengthening of TsD. This limit has not yet been observed because experiments have not been carried out at sufficiently low temperatures.

5. sunlrnary When starting this study we had four questions: ( 1) How should the motions revealed by the T,,

measurements be interpreted? (2 ) Is the branching of the T*2T level-crossing frequency related to the lifting of the 2T degeneracy? ( 3 ) Do the splittings of the type II ions fall below or above the studied range 5-60 MHz and is the unpaired T, minimum related to them? (4) What is T,, in (NH,),ZnCI,? During the present work we observed three unexpected results: the rise and fall of the anisotropy in M2, the maximum in T,, at 12 K and the shortness of T,, relative to T,, at the lowest temperatures. Many of these features can separately be explained in more 565

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than one way, and the joint explanation proposed here may not be the most probable in individual cases but gives the best overall account. The ammonium ions at the two non-equivalent sites reorientate at different rates and with some anisotropy, the type I ions being more hindered. The T,o minimum at 36 K as well as the shallower Mz step are caused by the slowing of the type I ions. The minimum in TID at 21 K is probably related to a level-structure change of the type I ions from A-TT-T-E to A-T-ZT-E with decreasing temperature, and the shoulder at 14 K should then be caused by the slowing of the type II ions. The big step in M2 below 20 K probably results from these events together. The anisotropy of A&, produced by the type I ions, is diminished by the various orientations of the type II ions as their non-tunneling motion becomes slower than the inverse line width. The maximum of T,, around 12 K is produced by the different motional rates of these two types of ions. The splittings of the type II ions are larger than those of the type I ions. The trigonal level structure A+T2T+ E of the type II ions does not contradict the fact that TsD< T,, at the lowest temperatures and fits well with the I& data. If we did not have the T,, results we would, however, choose the scheme A-3T-E or seek for still another explanation not involving highly distorted sites for the type II ions. Any structure with a level separation of 65 MHz could be responsible for the level-crossing minimum in T, near 32.5 MHz at 20 IL

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References

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