EISEVIER Physica B 233 (1997) 179-186

Neutron incoherent scattering study of NH3 low-energy transitions in hexammine compounds II

J. Mayer”, J.A. Janik”**, J. Krawczyka, K. Otnesb, 0. Steinsvollb, T. Stanek” “H. Niewodniczaiski Institute of Nuclear Physics, ul. Radzikowkiego 152, 31-342 Krakdw Poland

‘Institute for energy technolog;): 2007 Kjeller. Norway ‘Faculty of Chemistry of the Jagiellonian University. 30-060 Krakdw, Poland

Received 12 June 1996; received in revised form 13 November 1996

Abstract

This paper presents a search for tunnel transitions of NH, groups in hexammine compounds above the phase transition at which classical rotation, i.e. hoppings over barriers to rotation, start. The substances under study are CCWH,),lL CNWW,I(NW2~ lNWH3)& and [Mg(NH,),](NO,),. The incoherent scattering of neutrons was chosen as the experimental method. The elastic incoherent structure factor was analysed. Its behaviour with temperature provided evidence of tunnel transitions occurring besides hoppings over the barrier. In case of [Co(NH,),]I, it was possible to detect directly two broad satellites of the elastic line in the scattering pattern, which provided the tunnel transition energy. This energy decreases when approaching the phase transition, on cooling, thus showing a soft mode type of behaviour. This means that the barrier to rotation of NH, groups increases gradually before it reaches a significantly higher value in the low-temperature phase.

Keywords: Neutron scattering; Tunneling; Reorientation; Phase transition

1. Introduction

The energy level scheme of an NH3 planar hin- dered rotator depends very much on the barrier to NH3 rotation, as seen from Fig. 1 [l]. For the zero barrier the energy levels are those of the quantum free rotator. It has been shown by the neutron scattering experiment that for hexammine com- pounds this situation is being realized in [Ni(NH&](PF& where the NH3 groups rotate around the Ni-N axes [2]. For the infinitely high barrier the energy levels are those of the harmonic oscillator. Hexammine compounds are all quite far

* Corresponding author

from the infinite barrier limit. It may be seen from Fig. 1 that for intermediate cases, i.e. finite barriers, characteristic tunnel splittings show up. The transitions corresponding to these splittings were detected by neutron inelastic scattering with a very narrow energy resolution (mostly by using the backscattering technique) for the low-temperature phases of many hexammine compounds [3-51. For instance, for [Ni(NH&]12 the value of 63 PeV was reported in Ref. [3] at 5 K which corresponded to the low-temperature phase. (More advanced ex- periments detect several peaks in this region which is not surprising since the NH3 groups are not equivalent in the low-temperature phase [6].)

To our knowledge there were no attempts to search for tunnel splittings above the phase

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180 J. Mayer et al. / Physica B 233 (1997) 179-186

K

3oc

(8) -ma:6

b 31

(4) b 21

b 20

a b C

b 21

d e

Fig. 1. Energy level scheme for a planar NH, rotator in a threefold potential barrier V,/k: (a) free rotator V. = 0, (b) Vo/k = 100 K; (c) I/,/k = 200 K; (d) Vo/k = 300 K; (e) infinite barrier (according to Klaajisen Cl]).

transition. There are two reasons of this lack of structure factor) in the vicinity of the phase data. Firstly, at temperatures higher than several K, transition connected with stopping of NH3 groups. the corresponding inelastic peaks are very much These minima were difficult to explain as long as smeared out due to anharmonic effects, and sec- the possibility of an additional inelastic component ondly, besides the tunneling there occur jumps over was not taken into account. For a direct observa- barrier (classical rotation) which dominate more tion of such a component the measurements with and more with the increasing temperature. the narrow resolution were carried out.

In this paper we discuss the influence which the tunnel transitions may have on scattered neutron spectra. The substances under study were FWNH&IIZ, CWNHddNW~~ CNiWbklI~ and [Mg(NH&](NO&. The two former substan- ces were subjected to measurements on two spec- trometers, whose energy resolutions were different. This gave us a possibility to obtain more conclusive information. The two latter substances were meas- ured only with a low resolution - thus the con- clusions are limited. For all four substances, when measured with the broad resolution, wide minima were observed for EISF (elastic incoherent

The available information about the substances is as follows.

[Ni(NH&]12: The phase transition between phase I (regular, Fm3m) and phase II (trigonal or monoclinic) occurs at 19.7 K. NH3 groups rotate in phase I (hoppings over barrier). In phase II this rotation ceases to exist. The tunnel split- tings as measured by inelastic neutron scattering (INS) amount to 82, 67 and 42 ueV in phase II at ca. 5 K [S]. The NH3 groups are evidently nonequivalent in this phase. The average barrier height is ca.320 K [4].

J. Mayer et al. / Physica B 233 (1997) 179-186 181

[Co(NH&]I,: The phase transition between I and II occurs at 20.9 K. The substance is isomor- phic with Ni(NH&]12. Tunnelling energies are sim- ilar to those for Ni(NH&]12: 80,60 and 45 ueV [S].

[Ni(NH&](NO&: The phase transition be- tween phase II (regular, Pa3) and phase III (orthor- hombic) occurs at ca.110 K, on cooling, and at ca.200 K, on heating. NH3 groups rotate in phase II. In phase III four out of six NH3 groups cease to rotate, but two still perform hoppings over barrier. The tunnel splittings as measured by INS in the low-temperature phase are 18.9 and 5.6 ueV [S].

[Mg(NH&](NO&: The phase transition be- tween phase II and III occurs at ca.110 K, on cool- ing, and at ca.145 K, on heating. The substance is isomorphic with [Ni(NH&](NO,), and has sim- ilar properties [7].

2. Experimental

The samples were in the form of a polycrystalline powder contained in a flat aluminium sample- holder. The thickness was ca. 1 mm, so that mul- tiple scattering effects could not be excluded.

One scattering run was carried out on the spec- trometer TOF installed at the reactor JEEP II at Kjeller, Norway. The incident neutron energy was 4.63 meV. The energy resolution, determined via scattering by Ni was ca. 140 ueV (HWHM). The measurements were performed for one scattering angle only (80”) which corresponded to the mo- mentum transfer 1.91&‘.

The second scattering run was carried out only for [Co(NH&j12 and for [Ni(NH,),](NO,), on the spectrometer NERA, installed at the pulsed reactor IBR-2 at Dubna, Russia. In these measure- ments the energy of scattered neutrons was fixed at 4.76 meV and the energy resolution was ca. 30 ueV. This was achieved by almost back scattering from a copper monocrystal. Measurements were per- formed for four scattering angles. Both at Kjeller and at Dubna the resolution function is well de- scribed by the slightly deformed (asymmetric) Gaussian function.

The background was assumed to be a straight line which connects the far lying parts of the wings of the scattered neutron spectrum.

We tried to treat the results as the QNS ones which could be characterized by the elastic incoher- ent structure factor (EISF). The neutron spectra (after background subtraction) were approximated by a Lorentzian plus delta function both convol- uted by the resolution function. The EISF was evaluated as a ratio of the area below the elastic part to the total area of the spectrum.

The fittings based on such an approximation were fairly good, although for [Co(NH&]12 their quality was bad for all temperatures corresponding to phase II (9, 12, 15 and 17 K) for measurements with narrow resolution. This is not surprising in view of what will be explained below.

3. Results

Figs 2-5 show the EISF versus temperature be- haviour for all four hexammine compounds under study. In all cases one observes a minimum in EISF, in vicinity of the phase transition to the low-temperature phase. This minimum indicates that there is in this region an excess of non-elastic intensity, visualized by a deficiency of the elastic component. Most of the experimental points cor- responding to measurements with the broad resolu- tion (ca. 140 ueV) were obtained at Kjeller. The corresponding momentum transfer is 1.91 A-’

0.5 I. 9. I, I. 1. I., I, I. I.,

o.ol,“‘lQ,“‘,‘,‘,‘,‘,“cl 14 16 18 20 22 24 26 28 30 32 34

Temperature [Kl

Fig. 2. EISF versus temperature for [Co(NH&JI,. Points cor- respond to measurements with low resolution. The phase I/phase II transition point, according to literature, is 20.9 K [l]. The line is a guide to the eye only.

182 J. Mayer et al. / Physica B 233 (1997) 179-186

. ..”

10 12 14 16 18 20 22 24 26 28 30 32

Temperature [Kl

Fig. 3. EISF versus temperature for [Ni(NH&i12. Points cor- respond to measurements with low resolution. The phase I/phase II transition point, according to literature, is 19.7 K [l]. The line is a guide to the eye only.

0.01 I c a a I 110 130 150 170 190 210 230

Temperature [Kl

Fig. 4. EISF versus temperature for [Ni(NH,),](NO,),. Circles - broad resolution, squares - narrow resolution. On cooling the phase II/phase III transition point, according to literature, is ca. 110 K [9]. The line is a guide to the eye only.

(circles). For [Ni(NH,),](NO,), we present also the experimental points obtained from measure- ments with the narrow resolution (ca. 30 ueV) at Dubna. The corresponding momentum transfer is 1.96 A-’ (squares). Multiple scattering cannot be excluded, but its contribution cannot change the general character of temperature behaviours. The results for [Ni(NH,),](NO& for the two resolu- tions corroborate each other, when the narrow resolution data are processed in the same manner as those of broad resolution, i.e. when the

0.01 f 1 a ’ a * ’ 8 0 t J 120 130 140 150 160 170 160 190 200 210

Temperature [Kl

Fig. 5. EISF versus temperature for [Mg(NH,),](NO,),. Points correspond to measurements with broad resolution. On cooling the phase II/phase III transition point, according to literature, is ca. 110 K [7]. The line is a guide to the eye only.

non-elastic part is assumed to be a QNS compon- ent approximated by a single Lorentzian (convol- uted by the resolution).

As already mentioned, the Lorentzian shape of the non-elastic part seems not to be adequate for [Co(NH&JI,. Therefore, we suggest another treat- ment of the scattering pattern (Fig. 6(a) and (b)). It was assumed that above the phase transition point the whole pattern is composed of the elastic part approximated by a slightly deformed Gaussian function, plus three Lorentzian functions - one representing the QNS component and two repres- enting inelastic shoulders on both sides of the elas- tic component due to (interpreted as connected with) tunnel transitions (Fig. 6(a)). Below the phase transition point i.e. for phase II, the QNS compon- ent was absent (Fig. 6(b)). The temperature depend- ence of the tunnel splitting AE is presented in Fig. 7. For temperatures up to ~30 K such treatment of the [Co(NH&]12 spectra leads to much better fittings (as judged by x2 test) than the treatment based upon an assumption that the “wings” are parts of the QNS component.

We observe a decrease of the average shoulder energy transfer when the temperature approaches the phase transition point from above. This may be treated as a soft mode behaviour. In phase II the average value is ca. 56 ueV and is in a rather good agreement with the values reported by Blank and

J. Mayer et al. / Physica B 233 (1997) 179-186 183

Co(NH+jJz T=22K Co(NH3)6Jz T=9K

T 700 II d 600

(a)

” 1 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

Energy tronsfer CmeVl

Fig. 6(a). Scattered neutron spectrum obtained with narrow Fig. 6(b). Scattered neutron spectrum obtained with narrow resolution at Dubna for [Co(NH&]I,. Temperature 22 K. resolution at Dubna for [Co(NH&]I,. Temperature 9 K. Phase Phase I. The curve which fits well to the points is composed of II The curve which fits well to the points is composed of a central slightly deformed Gaussian - representing the elastic a slightly deformed Gaussian-representing the elastic compon- component, and of three Lorentzians - the central one repres- ent, and of two shoulder Lorentzians. No QNS component is enting the QNS component plus two shoulders. present.

1000

900

600

? 700 3 D 600

x ;c-' 500

s 400

E - 300

0 I

-0.2 -0.1 0.0 0.1 0.2

(b) Energy transfer ImeVl

1. ,. I. I. ,, ,,I. I. I. I .I

220 -

200 -

180 - $

z

160 -

.3 140 -

4

120 -

100 -

80 -

ii.~

60 -3 T T

40 -

10 12 14 16 18 20 22 24 26 28

Temperature [Kl

Fig. 7. Temperature dependence of the mean tunnel energy splitting AE, for [Co(NH&jI,. Error bars contain both the differences between the left shoulder and right shoulder peak positions, and the standard errors of fitting procedures.

Kearley [S], 80, 60 and 45 ueV, which were ob- tained with a still higher resolution.

From Fig. 7 we may deduce that the phase I/phase II transition occurs a little below 18 K i.e. below the 20.9 K value quoted from literature in

Section 1. The value below 18 K is however valid for our sample, as shown in Fig. 8 presenting the neutron diffraction spectrum measured simulta- neously. The difference may perhaps be attributed to a systematic error of temperature measurements.

184 J. Mayer et al. / Physica B 233 (1997) 179-186

6000

0’ ’ I

1.50 1.55 1.60 1.65 1.70

dhkl [AI

Fig. 8. Neutron diffraction patterns obtained simultaneously with the spectra of Figs. 6(a) and (b). Phase I - 22 - 15 and 12 K.

K and 18 K, phase II

4. Discussion

The minimum in EISF is due to an extra inelastic intensity caused by transitions between tunnel splitted levels. These transitions compete with hop- pings over barriers at sufficiently low temperatures. At higher temperatures they are dominated by hop- pings i.e. by classical reorientations. The scenario on cooling would thus be: At high temperature, the major role in NH3 dynamics is played by classical NH3 jumps over the barrier. These lead to a quasielastic component (central Lorentzian in Fig. 6(a)) besides the purely elastic one (Gaussian in Fig. 6(a). But, since for each NH3 group there exists an energy level scheme such as in Fig 1, there occur when the temperature decreases, less hoppings over the barriers, and hence the transitions between splitted levels (tunnellings) become visible. These transitions lead to inelastic peaks situated on both sides of the elastic peak, corresponding to scatter- ing with energy gain and energy loss. These peaks (shoulders) are smeared out by, firstly the resolu- tion, and, secondly the temperature. In our treat- ment of data they are approximated by “shoulder” Loreztzians in Figs 6(a) and (b). For measurements

with (low) broad resolution these shoulders are so smeared out that they “pretend” to be parts of the QNS component, which thus seems to have an anomalously high intensity (dip in EISF). When the temperature is sufficiently high, the classical re- orientation dominates and no anomalous EISF behaviour is observed. If this is true, the EISF minimum should disappear when the intensity of satellites is not taken into consideration when cal- culating EISF (i.e. when taking into consideration only the central QNS component). In the low- temperature phase of [Co(NH3),]12 the so evalu- ated EISF is equal to one, since in this phase there is no central QNS component. In the high-temper- ature phase EISF values evaluated from central QNS component only show a relatively large scatter (within the limits from 0.49 to 0.64) but no system- atic temperature dependence. Thus, we may claim that there is no minimum but only a jump of EISF from a value of ca. 0.57 (average) to the value of 1 when passing from phase I to phase II on cooling.

It has to be pointed out that the quality of deconvolutions of the spectra in phase I of [Co(NH,),]I, improves considerably when the sat- ellites are taken into account.

J. Mayer et al. / Physica B 233 (1997) 179- 186 185

It is remarkable that indirectly -. via the minimum of EISF - we are able to observe the effect of tunnell- ing even at temperatures as high as above 100 K for CWNH&I(NW~ and CMgW%M(NO&. The minima of EISF are, however, relatively shallow for these two substances because of two reasons: First- ly, the high-temperature smears the neutron spectra out, and, secondly, the tunnel splittings are much smaller than for [Co(NH&]I, and [Ni(NH3)J12. The high resolution does not help, but it is fortu- nate that the Kjeller and Dubna results corrobor- ate each other.

As seen from Fig. 7 the tunnel splitting for NH3 groups in [Co(NH,),]I, at 22 K (phase I) amounts to 140 ueV, which corresponds to a barrier height to rotation of ca. 250 K.

It may be seen from Fig. 7 that inspite of gradual decrease of the tunnel splitting when approaching the phase transition (on cooling) there is a jump of the splitting value at the transition. Thus the transition is of the first order.

We should admit that the estimated tunnel transition contributions seem too large, but this may be connected with our choice of the back- ground, which may be different from unknown real one.

The soft mode behaviour of the tunnel transition mode indicates on cooling a gradual increase of the barrier when the phase transition is being ap- proached. This probably corresponds to the grad- ual slowing down of reorientations as observed by Eckert and Press for [Ni(NH3)J2 [3].

5. Estimation of multiple scattering effects

For this purpose the standard procedure (as used for instance at RAL) has been applied [S]. The procedure provided the single scattering spectra from the experimentally measured ones, for which it was assumed that they contain the single scattering events plus the double scattering ones. In addition, the measurements with the broad resolution were made for a few temperatures with lJ$(NH,)],(NO,), thin sample (0.3 mm), for which the multiple scat- tering is very much reduced (but at the same time the scattered intensity is low). It was proved that

the single scattering spectra obtained by computa- tion from the standard procedure are very nearly the same as those obtained without the multiple scattering correction with the 0.3 mm sample. The corrected and uncorrected data for [Co(NH,),]I, and [Ni(NH&](NO,), are shown in Fig. 9. It should be pointed out that taking into account the multiple scattering effects improves the sym- metry of satellites positions on both sides of the

0.7 I. I. I. I .,.I.,.,.,.,. i“).

0.6 ~:

0.5 -

k 0.4 -

w 0.3 -

0.2 -

0.1 -

14 16 16 20 22 24 26 28 30 32 34

(a) Temperature tK1

Fig. 9(a). EISF versus temperature for [Co(NH&]I, corrected for multiple scattering: (0) corrected points obtained by compu- tation from the uncorrected data (0) (the same as in Fig 2). The line is a guide to the eye only.

I 0

0.1 II . Kjellerofter MUS cow. + Kjeller0.3 mm sample

0.0 ’ I 110 130 150 170 190 210 230

(b) Temperature [Kl

Fig. 9(b). EISF versus temperature for [Ni(NH,),](NO,), cor- rected for multiple scattering: (0) corrected points obtained by computation from the uncorrected data (0) (0 and ??the same as in Fig. 4). ( + ) points obtained from the thin (0.3 mm) sample without the multiple scattering correction. The line is a guide to the eye only.

186 J. Mayer et al. / Physica B 233 (1997) 179- I86

central peak. For Co(NH&12 at 22 K the positions without the multiple scattering correction are: - 130 ueV and + 170 ueV, whereas with the cor-

rection they are:- - 152 ueV and + 154 ueV. It is evident that the multiple scattering effects

are present in our results, but they do not deform them to any significant degree, causing only a more or less parallel shift of the EISF versus temperature dependence towards somewhat larger values of EISF. Thus the discussion as based on the uncor- rected data of Figs. 2-6 should be valid.

Acknowledgements

Our thanks are due to Dr. Wojciech Zajgc for his help in applying the RAL multiple scattering pro- cedure to our results. We are grateful to the late Prof. Janina Janik for her help in the measurements with CNW-LM(NW~~ CMgWMdNW~ and CWNH&lL y and to the late Prof. Tormod Riste

for very stimulating discussions. One of us (J.A.J) thanks the Institutt for energiteknikk at Kjeller, Norway, for the financial help enabling his stay in Norway.

This work was partly financed by the Committee for Scientific Research (KBN), grant No.2-P302- 118-06.

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(1987) 5989. [3] J. Eckert, W. Press, J. Chem. Phys. 73 (1980) 451. [4] W. Press, J. Eckert, J. Chem. Phys. 67 (1977) 5752. [S] H. Blank, G.J. Kearley, J. Chem. Phys. 87 (1987) 6809. [6] A.R. Bates, K.W. Stevens, J. Phys. C2 (1969) 1573. [7] J.M. Janik, J.A. Janik, A. Migdal-Mikuli, E. Mikuli, K.

Otnes, Physica B 168 (1991) 45. [S] M.W. Johnson, Harwell Report AERE - R 7682 (1974). [9] J.A. Janik, J.M.Janik, A. Migdal-Mikuli, E. Mikuli, K.

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