J. Phys. Chem. B 1999, 103, 4109-4112 87Rb
4109
NMR Studies of Molten and Glassy 2Ca(NO3)2-3RbNO3 C. Zu1 rn, A. Titze, G. Diezemann, and R. Bo1 hmer* Institut fu¨r Physikalische Chemie, Johannes Gutenberg-UniVersita¨t, 55099 Mainz, Germany ReceiVed: October 1, 1998; In Final Form: January 20, 1999
Calcium rubidium nitrate, 2Ca(NO3)2-3RbNO3 (CRN), has been studied in its molten and glassy states using 87 Rb NMR techniques. In the solid phase asymmetric and smeared quadrupole perturbed spectra of the central Rb resonance reflect a highly disordered ionic local structure. At low temperatures, T < 80 K, the spinlattice relaxation times follow a power law, T1 ∝ T-R with R ) 3. A local T1 minimum near T ) 145 K reveals the slow down of the 3-fold rotation of the planar nitrate group. The NMR results are compared with the conductivity relaxation in CRN.
I. Introduction Molten nitrate salts have long provided a much-used testing ground for models and theories of the vitrification process. The emphasis of many studies has been either on the calorimetric glass transition near Tg,1 or on the critical temperature, TC, of mode coupling theory.2 Particularly well studied are the glass formers of the 2MII(NO3)2-3MINO3 family with MI denoting a monovalent ion (e.g., Na, K, or Rb) and MII denoting a divalent one (e.g., Mg, Ca, or Sr). The calorimetric glass transition temperature Tg of these substances like, e.g., 2Ca(NO3)2-3KNO3 (CKN, Tg ) 333 K) and the isostructural compound 2Ca(NO3)2-3RbNO3 (CRN, Tg ) 333 K) is just above room temperature.3 Therefore, the ionic conduction4-6 in the melt as well as the excitations in the amorphous solid state7,8 can conveniently be studied. A schematic representation of the glass structure that has been suggested9 for CKN on the basis of diffraction data is shown in Figure 1. Its basic building block is a Ca2+ ion tetrahedrally coordinated by four NO3- ions. Each NO3 group can be shared either directly by two adjacent tetrahedra or it can be close to a monovalent cation which in turn is attached to another NO3 group. For the composition 2Ca(NO3)2-3KNO3, one out of four nitrate groups is shared directly. It has been emphasized previously that apart from the structural relaxation10 a number of processes exist in CKN that sequentially decouple from the primary relaxation upon cooling from the high-temperature molten state. A relaxation map combining results from CKN and CRN is given in Figure 2. Near the glass transition the ion transport as well as the local ion exchange11 dynamics are only loosely coupled to the structural relaxation. In CKN and related compounds the ratio of structural relaxation time τC ()100 s at Tg) to the conductivity relaxation time τσ is about 10 000.3 The decoupling ratio R ) log(τC/τσ) ) 4.1 (ref 3) in the nitrate melt CRN is intermediate between the fast ion conductors with R ≈ 12 and fully coupled melts such as SiO2, where near Tg the conductivity and structural relaxation times are very similar (R ≈ 1).12 There are only a few ionic conductors which show an intermediate decoupling.4,13 The narrowing of the electrical modulus spectra9 reported for these materials upon approaching Tg from above is opposite to the trend commonly seen in the width of structural relaxation spectra.14 This combination of properties, on one hand, makes substances such as CKN test cases to study the decoupling issue.15 On the other hand, the loose coupling in this and related
Figure 1. Schematic representation of the glass structure of CRN. The Rb ions are represented by the black dots. The nitrate ions (in gray) are seen in various orientations. The tetrahedra are meant to represent the cages formed by the four nitrate groups around each calcium ion. The calcium ions themselves have been omitted for clarity. The sizes of the ions are not drawn to scale. Sketched after ref 9.
molten salts enables to monitor the structural relaxation via conductivity studies.16 Apart from the translational and vibrational motions, in CKN rotational degrees of freedom have received particular attention. The rotational dynamics of the planar, triangular nitrate group has been studied using Raman scattering,17 transient optical Kerr effect measurements,18 quasielastic neutron scattering,19 and nuclear magnetic resonance (NMR).20 From the latter study which employed the 15N probe it was concluded that the molecular nitrate ion performs a rapid reorientation around its 3-fold (C3) axis. As also seen in the Raman investigation this motion appears to take place on the sub ps scale even at Tg. The 15N NMR investigation has shown additionally that the time scale governing the tumbling motion of the C3 axis itself scales with that describing the structural relaxation.20 While the 15N nucleus is well suited to study the dynamics in the liquid state the spin-lattice relaxation times T1 become prohibitively long when approaching Tg. In order to gain insights into the dynamics of the glassy state as well we have studied 2Ca(NO3)2-3RbNO3 using 87Rb-
10.1021/jp9839246 CCC: $18.00 © 1999 American Chemical Society Published on Web 03/12/1999
4110 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Figure 2. Relaxation map of the molten nitrates CKN and CRN. Part of the figure was adapted from ref 6. The T1 maxima from the present investigation on CRN are marked by the crosses and are shown to appear at τ ) 1/ωL. The data for the conductivity σ are from ref 4 (CKN) and ref 3 (CRN). Relaxation times τ from primary (R, ref 10) and several decoupled processes [secondary process (β),7 nitrate rotation (NO3),15 and local ion exchange (η)11] are for CKN. The dashed lines are guides to the eye. The dash-dotted line represents an Arrhenius law τ ) τ0exp(ENO3/RT) with log (τ0/s) ) 12.5 and ENO3 ) 12.5 kJ/ mol (ref 17).
Zu¨rn et al.
Figure 3. Double-logarithmic representation of the spin-lattice relaxation time T1 versus T. At low temperatures the straight line indicates a power law 1/T1 ∝ TR with an exponent R ) 3. The arrow at T ) 145 K marks the local maximum seen in 1/T1. Above Tg the rate sharply rises and reaches another maximum near 390 K.
NMR. As a quadrupolar nucleus (I ) 3/2) the Rb probe is particular sensitive to the motions of ionic charges in its vicinity. Spin 3/2 nuclei are of course also advantageous when investigating the liquid state and previously they have been used to study molten MINO3 salts with MI ) Li, Na, and Rb.21 2. Experimental Details Highly pure (> 99.9%) ingot chemicals [Ca(NO3)2-4H2O and RbNO3 from Johnson Matthey Co. and Aldrich Co.] were mixed in appropriate fractions, slowly heated to about 470 K, fused for several hours, and rapidly cooled to room temperature. The nitrate glasses were then powdered and filled into glass tubes under the dry N2 atmosphere of a glovebox. Finally, the sample tubes were evacuated and flame sealed. The 87Rb-NMR measurements were carried out at a Larmor frequency of ωL/ 2π ) νL ) 85.7 MHz using a home-built spectrometer. The π-pulse typically was 2.5 µs long. Central transition spectra were obtained with fixed refocusing delays of 30-100 µs. This is much shorter than the spin-spin relaxation times T2. Below room-temperature transversal dephasing was found to be single exponential and it took always longer than about 350 µs. Spinlattice relaxation times were measured using an inversion recovery sequence. Above Tg the longitudinal magnetization was read out using a π/2 pulse. Below Tg a solid echo was used for this purpose. A variable temperature insert from Oxford Instruments was employed in conjunction with a LakeShore 330 temperature controller to stabilize the measurement temperatures. In the entire accessible range a stability of better than ( 0.1 K was achieved. Measurements on two independently prepared specimens gave results that were identical within experimental error. The results also did not depend on whether data were collected on heating or on cooling.. 3. Results The longitudinal magnetization decay M(t) was measured in a temperature range from about 10 to 500 K. It could always be described using a Kohlrausch function, M(t) ∝ exp[-(t/ T1)1-ν]. This functional form involves the stretching exponent (1 - ν) and is commonly used in the literature to describe nonexponential magnetization decays.22 In Figure 3 we present a double-logarithmic plot of the spin-lattice relaxation rate,
Figure 4. Nonexponentiality parameter ν characterizing the longitudinal magnetization recovery as a function of temperature. The typical error is roughly given by the size of the symbols, except in the temperature range from Tg to T ≈ 400 K. Here the uncertainty of ν is somewhat larger.
1/T1, versus temperature. At temperatures below about 80 K this representation shows directly the existence of a power-law, 1/T1 ∝ TR, with an exponent R ) 3.23 Then at somewhat higher temperatures a local rate maximum is found near T ) (145 ( 10) K. This maximum indicates the slow down of fluctuations in the electrical field gradient (EFG) tensor at the Rb site and hence of ionic motions in the vicinity of the nuclear probe. The fact that near 145 K only a local maximum exists indicates that the ionic motions giving rise to the rate maximum are highly anisotropic. Although it is not emphasized by the logarithmic representation of Figure 3 it should be realized that the rate maximum is very broad and T1 changes by less than a factor of 2 in the wide temperature range between 80 K and Tg. Above this temperature the rate rises sharply and exhibits a maximum near 390 K. As will be discussed in more detail in section 4, below, this maximum is the signature of structural relaxation and indicates that the R-relaxation takes place on the time scale set by the Larmor frequency. In other terms, above Tg isotropic EFG fluctuations at the Rb site give rise to a very efficient averaging of the quadrupolar interactions resulting in a global rate maximum. The slow down of the structural relaxation near Tg yields an essentially frozen ionic structure. Then in the glass only the rotational motions of the nitrate groups lead to a residual modulation of the quadrupolar interactions. The amplitude of this modulation is quite small. This can be inferred from the fact that the rates at the two maxima differ by about 2 orders of magnitude. The nonexponentiality parameter ν is shown in Figure 4. In the limit of fast R-relaxation (as compared to the Larmor
Molten and Glassy 2Ca(NO3)2-3RbNO3
Figure 5. Quadrupole perturbed absorption spectra of the 1/2 f -1/2 transition of the 87Rb resonance of CRN represented as lines.
frequency) ν vanishes within experimental error, indicating single-exponential recovery. Then, below the rate maximum the magnetization recovery exhibits an increasing stretching. Below about Tg the exponent ν turns almost constant. We find ν ) 0.42 ( 0.05 with a slight tendency to increase with decreasing temperatures. The general temperature dependence of ν is thus quite similar to that deduced from the nonexponentiality of the longitudinal deuteron magnetization recovery of supercooled liquids and amorphous polymers in the undercooled and glassy regimes.24 Solid echo spectra are shown in Figure 5 for two temperatures. The spectrum taken near room temperature is somewhat narrower than that recorded at 87 K. This slight increase in line width is presumably due to the freeze-out of the dynamic processes giving rise to the local T1 minimum at 145 K. The asymmetric broadening indicates a second-order line shift of the central 1/2 f -1/2 transition of the 87Rb resonance. The absence of pronounced edge singularities reveals that the EFG tensors are not well defined in the sense that a distribution of quadrupole couplings and most likely also of asymmetry parameters η is present.25 With the maximum possible separation of the edge singularities taken to be ∆ν ) 200 kHz, a maximum quadrupolar coupling constant νQ ) (νL∆ν144/75)1/2 of about 6 MHz can be estimated if η ) 0 is assumed. For η * 0 similar νQ are obtained. Coupling constants of several MHz are typical for the 87Rb probe.25 4. Discussion First, we discuss the nonexponentiality of the magnetization recovery in the glassy state. When essentially exciting the central transition of the Rb resonance each site should in general exhibit an approximately biexponential M(t). However, in a disordered solid the ionic correlation time will not be uniform. In addition there is a distribution of field gradients at the nuclear sites. From the combination of all these effects a broad distribution of spinlattice relaxation times V(T1) can be expected. This distribution gives rise to a smeared magnetization recovery at temperatures T < Tg for which the quadrupolar interactions are not averaged out by fast ionic motions, cf. Figure 4. In the glass transformation regime additional effects come into play. Particularly important is the averaging of the T1-distribution which is induced by the structural relaxation. This leads to an decrease of the exponent ν similar to what is known from deuteron NMR investigations on supercooled liquids24 and disordered crystals.26 However, different from what is known from 2H NMR, in our case the intrinsic magnetization recovery is not single exponential and additionally a distribution of field gradients is to be expected. These circumstances hamper a straightforward quantitative interpretation of the stretching exponents from our 87Rb study. At first glance the temperature dependence of the spin-lattice relaxation rate shown in Figure 3 resembles the pattern seen
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4111 from investigations of the dielectric loss of supercooled liquids.27 There, usually two peaks are observed. The larger and narrower one is associated with the structural or primary relaxation. The smaller and broader one is often assigned to a secondary or Johari-Goldstein process.27 For CRN, the global rate maximum, which via the fluctuation-dissipation theorem may be read as the imaginary part of a generalized susceptibility, χ′′(ωL), indeed signals the slow down of structural relaxation on the NMR time scale. However, as we will show below the secondary rate maximum is not due to a Johari-Goldstein process. It is due to a local relaxation process which is specific for the molten nitrates. The 1/T1 maxima evident from Figure 3 indicate that the characteristic correlation time associated with the ionic motions dominating spin-lattice relaxation is on the order of the inverse Larmor frequency, i.e., ωLτNMR ≈ 1. In Figure 2 this time scale from NMR is compared with the conductivity relaxation time τσ. A close inspection reveals that, above Tg, τσ is very slightly longer than τNMR (ref 28). This observation is different from those made for ion conducting glasses characterized by a large decoupling index.15 The near equality of τσ and τNMR for CRN can be rationalized by noting that unlike the situation encountered in fast ion conductors in the molten salt the slow down of the global ionic restructuring as observed using NMR occurs not much below but rather much above Tg. In the high temperature melt obviously the translational motions of all ionic species which give rise to spin-lattice relaxation do also take part in the structural relaxation. Here the only motion which does contribute neither to ionic conductivity nor to the restructuring associated with the primary relaxation is the reorientational motion of the NO3 group. Above room temperature the C3-rotation of the nitrate group has been studied by a number of techniques for CKN.17-20 A particularly wide temperature range (302 K < T < 610 K) has been covered by depolarized Raman scattering.17 When extrapolating the reorientation rates from this study we find that near T ) 150 K they should be on the order of the Larmor frequency employed for the present investigation (cf. Figure 2). As Figures 2 and 4 show near 150 K the rate 1/T1 indeed exhibits a maximum in the related glass former CRN. Although this comparison involves a substantial extrapolation of the Raman results, they agree well with those from NMR. This agreement strongly corroborates our finding that the local T1 minimum is due to the slow down of the C3 nitrate rotation on the NMR time scale and that the C3 motion of the NO3 groups dominates spin-lattice relaxation, at least for 100 K < T < 300 K. This interpretation is fully consistent with the glass structure shown in Figure 1. There it can be seen that the nitrate groups due to their close proximity to the nuclear probes will dominate the EFG fluctuations at the Rb sites. Furthermore, the substitution of the monovalent cation K by Rb is not seen to have a major impact on the local reorientation processes in the glassy nitrates. The broad local maximum in 1/T1 indicates the presence of a broad distribution of spin-lattice relaxation times and hence of a wide distribution of time scales which describe the ionic motions. Recently, it could be shown using 15N NMR that the distribution concept is indeed valid for the supercooled liquid state of the nitrates.20 That study revealed that the tumbling motion of the C3 axes of the nitrate ions, taking place on the time scale of the R-relaxation, proceeds in a heterogeneous fashion, i.e., it involves a distribution of correlation times.29 This heterogeneity may be seen as a precursor of that characterizing the glassy state. Below Tg we are concerned with the dynamic heterogeneity of the C3 rotation of the nitrate groups taking place in the local potentials set up by the vitrification process. It is
4112 J. Phys. Chem. B, Vol. 103, No. 20, 1999 plausible to assume that the broad distribution of ionic correlation times (or nitrate rotation times) observed in our study in turn is due to a distribution of local energy barriers g(E). To test this idea we have calculated the average spin-lattice relaxation time as 〈T1〉 ) ∫dEg(E)[1/J(ωL)+1/J(2ωL)]/K with the spectral density J(ω) ) τ(E)/[1+ω2τ2(E)], the correlation time τ ) τ0exp(E/RT) and the quadrupolar coupling K. A box distribution for g(E) which is only nonzero for 0.1 < E/ENO3 < 1.25 roughly reproduces the experimental T1 in the range 100 < T < 300 K (not shown).30 At lower temperatures 1/T1 is much longer than anticipated from these calculations indicating that here additional excitations may come into play. For temperatures 10 K < T < 100 K the spin-lattice relaxation of numerous glass formers is reported to be due to thermally activated excitations in asymmetric double well potentials.31 For this type of excitation, which is typical for highly disordered solids, one expects 1/T1 ∝ TR with R ≈ 1 but occasionally much larger exponents have been observed (e.g., R ) 2 for amorphous As2S3).22 Via the fluctuation-dissipation theorem 1/T1 has been related to the frequency and temperaturedependent electrical conductivity, σ(ω,T) ∝ ω2/[T1(ω,T)T]. Applying this relation to our results (R ) 3) one would predict that σ ∝ T2. While the conductivity data to check this proposal for CRN are not available, corresponding results in the glass former CKN show that σ does not exhibit a quadratic temperature dependence. Merely, in the relevant temperature range a dielectric relaxation process of unknown origin shows up.11,32 To understand the mechanism giving rise to the low-temperature spin-lattice relaxation of CRN further work is needed. 5. Conclusions Using 87Rb-NMR we have studied the ion dynamics in the fragile glass-former 2Ca(NO3)2-3RbNO3 covering a wide temperature range, 8 K < T < 500 K. The temperaturedependent spin-lattice relaxation rate exhibits two maxima. When comparing with results from impedance spectroscopy6 the maximum seen near 390 K reveals that the ionic motion causing the structural relaxation and the conductivity relaxation take place on about the same time scale. This finding is to be distinguished from a decoupling of these two processes found in most fast ion conductors.12 The absence of significant conductivity decoupling in CRN at 390 K is consistent with the previous observation that noticeable cooperative phenomena emerge only below the temperatures at which the global rate maximum shows up.16 Also below 390 K the longitudinal magnetization recovery turns nonexponential. It can be described by a Kohlrausch function with a parameter ν which below Tg is in the range ν ) 0.42 ( 0.05. The very broad rate maximum showing up near 145 K, i.e., deep in the glassy phase, is due to the slow-down of the 3-fold rotation of the planar nitrate molecular ion in a highly disordered local environment. Comparison with previous Raman experiments on the structurally related glass-former CKN reveals that the nitrate rotation is quite insensitive to the size of the monovalent cation. 17 We have shown that a change in temperature from 294 to 87 K leaves the asymmetrically broadened central transition spectra of the 87Rb resonance in CRN almost unchanged. This confirms that the average local structure seen by the nuclear probe is frozen in below room temperature. At low temperatures, T < 80 K, the spin-lattice relaxation rate follows a power law 1/T1 ∝ TR. We find an exponent R ) 3 which in comparison with other glassy materials 22,31 is unusually large. Acknowledgment. One of us (R.B) is greatly indebted to Austen Angell for the stimulation he provided when working
Zu¨rn et al. in the field of glass-forming melts under his generous and enthusiastic guidance. N. Bu¨ttgen and E. Skoplaki are thanked for their contributions in the early stages of this work. The Deutsche Forschungsgemeinschaft supported this project financially under Grant SFB262-D9. References and Notes (1) Angell, C. A. J. Phys. Chem. 1964, 68, 218. Williams, E.; Angell, C. A. J. Phys. Chem. 1977, 81, 232. (2) Cummins, H. Z.; Du, W. M.; Fuchs, M.; Go¨tze, W.; Hildebrand, S.; Latz, A.; Li, G.; Tao, N. J. Phys. ReV. E 1993, 47, 4223. Kartini, E.; Collins, M. F.; Collier, B.; Mezei, F.; Svesson, E. C. Phys. ReV. B 1996, 54, 6292. Yang, Y; Nelson, K. A. J. Chem. Phys. 1996, 104, 5429. Lunkenheimer, P. Pimenov, A.; Loidl, A. Phys. ReV. Lett. 1997, 78, 2995. (3) Pimenov, A.; Lunkenheimer, P.; Nicklas, M.; Bo¨hmer, R.; Loidl, A.; Angell, C. A. J. Non-Cryst. Solids 1997, 220, 83. (4) Howell, F. S.; Bose, R. A.; Macedo, P. B.; Moynihan, C. T. J. Phys. Chem. 1974, 78, 631. (5) Cramer, C.; Funke, K.; Buscher, M.; Happe, A.; Saatkamp, T.; Wilmer, D. Phil. Mag. B 1995, 71, 713. (6) Pimenov, A.; Lunkenheimer, P.; Rall, H.; Kohlhaas, R.; Loidl, A.; Bo¨hmer, R. Phys. ReV. E 1996, 54, 676. (7) Sokolov, A. P.; Ro¨ssler, E.; Kisliuk, A.; Quitmann, D. Phys. ReV. Lett. 1993, 71, 2062. (8) Mai, C.; Etienne, S.; Perez, J.; Johari, G. P. Philos. Mag. B 1985, 50, 657. (9) Wang, Y. B.; Ryan, D. H.; Altounian, Z. J. Non-Cryst. Solids 1996, 205-207, 221. and references therein. (10) Pavlatou, E. A.; Rizos, A. K.; Papatheodorou, G. N.; Fytas, G. J. Chem. Phys. 1991, 94, 224. (11) Bo¨hmer, R.; Sanchez, E.; Angell, C. A. J. Phys. Chem. 1992, 96, 9089. (12) Angell, C. A. Chem. ReV. 1990, 90, 523. (13) Hasz, W. C.; Moynihan, C. T.; Tick, P. A. J. Non-Cryst Solids 1994, 172-174, 1363. (14) But also seen in the conductivity relaxation of several other ion conductors, e.g., see: Hodge, I. M.; Angell, C. A. J. Chem. Phys. 1977, 67, 4. Leheny, R. L. Phys. ReV. B 1998, 57, 10537 as well as ref 13. (15) Tatsumisago, M.; Angell, C. A.; Martin, S. W. J. Chem. Phys. 1992, 97, 6968. (16) Pimenov, A.; Loidl, A.; Bo¨hmer, R. J. Non-Cryst. Solids 1997, 212, 89. (17) Jacobsson, P.; Bo¨rjesson, L.; Hassan, A. K.; Torell, L. M. J. NonCryst. Solids 1994, 172-174, 161. Bo¨rjesson L. (private communication). (18) Ricci, M.; Foggi, P.; Righini, R.; Torre, R. J. Chem. Phys. 1993, 98, 4892. (19) Kamiyama, T.; Shibata, K.; Suzuki, K.; Nakamura, Y. Phys. B 1995, 213, 214, 483. (20) Sen S.; Stebbins, J. F. Phys. ReV. Lett. 1997, 78, 3495. Sen S.; Stebbins, J. F. Phys. ReV. B 1998, 58, 8379. (21) Wolney Filho, W.; Havill, R. L.; Titman, J. M. J. Magn. Reson. 1982, 49, 296 and references therein. (22) Devreux F.; Malier, L. Phys. ReV. B 1995, 51, 11344 and references therein. (23) Note that R ) 3 has also been found for Na-β-alumina, albeit at somewhat lower temperatures (1.5 < T < 6 K), Sieranski, H.; Kanert, O.; Backens, M.; Strom, U.; Ngai, K. L. Phys. ReV. B 1993, 47, 681. (24) Do¨β, A.; Hinze, G.; Diezemann, G.; Bo¨hmer, R.; Sillescu, H. Acta Polymer. 1998, 49, 56 and references therein. (25) Freude D.; Haase, J. In NMRsBasic Principles and Progress; Springer Berlin, 1993; Vol. 29. (26) Bo¨hmer, R.; Fujara, F.; Hinze, G. Solid State Commun. 1993, 86, 183. (27) Johari G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (28) Using the relationship ωLτNMR ) 0.61 enhances the apparent difference between τNMR and τσ by 0.2 on a logarithmic scale. (29) For recent reviews dealing with the heterogeneity near Tg, see; Sillescu, H. J. Non-Cryst. Solids 1999, 243, 81. Bo¨hmer, R. Current Opin. Solid State Mater. Sci. 1998, 3, 378. (30) The parameters chosen for our calculations are ENO3 ) 12.5 kJ/ mol (ref 17), log(τ0/s) ) 12.5, and νQ ) (2π × 3 MHz)2. Somewhat less satisfying results were obtained using a Gausssian distribution of energy barriers. (31) e.g., Lu, X.; Jain, H.; Kanert, O.; Ku¨chler, R.; Dieckho¨fer, J. Philos. Mag. B 1994, 70, 1045. (32) Hayler L.; Goldstein, M. J. Chem. Phys. 1977, 66, 4736. From Figure 7b of this article which contains audio frequency dielectric measurements on CKN it can be seen that loss peak maxima show up near 50 K. The relaxation times estimated from these results are at least two decades shorter than those extrapolated from the NO3 rotation data as shown in Figure 2 of the current article. Hence it appears unlikely that the process seen near 50 K is directly related to the rotation of the nitrate groups.
