1 Introduction

The family of alkali trihydrogen selenite crystals of the type MeH3(SeO3)2 (Me=Li, Na, K, Rb, Cs, and NH4) is one of the most interesting families of hydrogen-bonded systems because of its structural peculiarities and physical properties [1–3]. The crystals of alkali metal trihydrogen selenites are an important group of hydrogen-bonded ferroelectrics that have very interesting properties. The crystals of the trihydrogen selenite family have no isomorphous structures, but the polar SeO3 2− groups are always linked by hydrogen bonds. One of them, KH3(SeO3)2, is unique in this family of compounds because it does not exhibit any ferroelectric or antiferroelectric properties [4]. KH3(SeO3)2 undergoes a second-order ferroelastic phase transition from a high-temperature orthorhombic phase with the space group D 142h -Pbcn to a low temperature monoclinic phase with the space group C 52h -P2 1 /b at the phase transition temperature T C = 211 K [5–11]. In this substance, there is a large difference between the T C of the hydrogen compound KH3(SeO3)2 and that of the deuterated compound KD3(SeO3)2; T C of KH3(SeO3)2 is 211 K and that of KD3(SeO3)2 is 302 K [12–19]. This large isotope effect suggests that the deuterium bond plays an important role in the phase transition of KD3(SeO3)2. Researchers in the fields of science and microelectronics have shown much interest in thin ferroelastic films [20–22] owing to the difference of their physical properties from those of the bulk material.

Grande et al. [15] reported the quadrupole parameters of 2H in KD3(SeO3)2 using nuclear magnetic resonance (NMR); the quadrupole coupling constant and asymmetry parameter were obtained below and above T C (=296 K) for O(3)–H···O(1) and O(2)–H···O(2) bonds. Blinc et al. [23, 24] reported the spin–lattice relaxation for 2H in KD3(SeO3)2 and concluded that there is a slowing down of the overdamped soft pseudospin-type deuteron mode. They also studied the 17O-proton nuclear double-resonance spectra of KH3(SeO3)2 below and above T C (=211 K) and the quadrupole coupling of all chemically inequivalent oxygen sites. Recently, the ferroelastic phase transition of KH3(SeO3)2 single crystals using NMR and ordering of the O(2)–D···O(2) bonds near the T C in KD3(SeO3)2 by 2H NMR was reported by our group [25, 26]. Although 1H and 2H NMR studies of KH3(SeO3)2 and deuterated KD3(SeO3)2 crystals in the laboratory frame have been reported, the phase transition mechanism of these two materials has not previously been studied using 1H and 2H magic angle spinning (MAS) NMR in the rotating frame.

We measured an MAS NMR spectrum of 1H and 2H in the rotating frame to investigate the role of hydrogen bonds in KH3(SeO3)2 and KD3(SeO3)2. In addition, the temperature dependences of the spin–lattice relaxation time in the rotating frame T 1ρ were obtained near T C. Measurements of T 1ρ by MAS NMR in the rotating frame are advantageous in that they allow for probing of molecular motion in the kilohertz range, whereas T 1 values by static NMR in the laboratory frame reflect motion in the megahertz range. The purpose of this study was to illuminate the nature of this phase transition using the chemical shifts and the spin–lattice relaxation time measurements for 1H and 2H MAS NMR.

2 Crystal Structure

KH3(SeO3)2 undergoes a second-order phase transition at T C = 211 K to a low temperature phase of space group P2 1 /b-C 52h . This transition is a pure pseudo-proper ferroelastic transition of the order–disorder type [27]. The SeO3 2− groups are linked by hydrogen bonds to double zigzag-shaped chains along the c- and a-direction. The SeO3 2− groups are linked by two different types of O–H···O hydrogen bonds. At room temperature, the structure of KH3(SeO3)2 belongs to the space group Pbcn-D 142h of the orthorhombic structure [28]. The unit cell has the parameters a = 16.152 Å, b = 6.249 Å, and c = 6.307 Å, and contains four formula units [8, 29]. The structure below T C is monoclinic and the unit cell parameters at low temperature are a = 16.130 Å, b = 6.206 Å, c = 6.257 Å, and α = 91.2° [10]. The unit cell dimensions of KH3(SeO3)2 and KD3(SeO3)2 crystals are the same within experimental error; the crystal structures of the undeuterated and deuterated compounds are isomorphous. The unit cell in the high-temperature phase of KH3(SeO3)2 is shown in Fig. 1 [30].

Fig. 1
figure 1

Structure of the paraelastic phase of KH3(SeO3)2 projected on the ac-plane. Dashed lines show the disordered hydrogen bonds

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3 Experimental Method

Single crystals of KH3(SeO3)2 were grown by the slow evaporation of an aqueous solution containing K2SeO3 and H2SeO3 at 302 K; the melting point of the crystals was about 343 K. The single crystals of KD3(SeO3)2 were grown by the slow evaporation method from a D2O solution of one mole of K2CO3 and four moles of SeO2. The melting point of the crystals was about 343 K. Both the undeuterated and the deuterated crystals were long, thin, colorless, and transparent.

In the rotating frame, 1H MAS NMR and 2H MAS NMR experiments were performed using a Bruker 400 FT NMR spectrometer at the Korea Basic Science Institute Seoul Western Center. The magnetic field was 9.4 T, and the 1H MAS NMR and 2H MAS NMR experiments were performed at Larmor frequencies of 400.125 MHz and 61.423 MHz, respectively. A Bruker MAS probe head with a 4-mm zirconia rotor was used. The MAS rate was set to 5 kHz for MAS, to minimize spinning sideband overlap. The chemical shifts for 1H and 2H were expressed with respect to tetramethylsilane (TMS). The spin–lattice relaxation times for 1H and 2H T 1ρ in the rotating frame were measured using π/2-t-acquisition, and T 1ρ were measured by varying the length of the spin-locking pulses. The π/2 pulse-times for 1H and 2H were 5 and 10 μs, respectively, corresponding to the spin-locking field strengths of 50 and 25 kHz. The temperature-dependent NMR measurements were obtained over a temperature range of 180–400 K. The samples were maintained at constant temperatures by controlling the nitrogen gas flow and the heater current.

4 Experimental Results and Analysis

Structural analysis of the protons in KH3(SeO3)2 was carried out by 1H MAS NMR spectroscopy. Figure 2a, b shows the chemical shifts of 1H MAS NMR spectrum in KH3(SeO3)2 as a function of temperature. The spinning sidebands are marked with asterisks. The signal at a chemical shift of δ = 12.6 ppm at 300 K was assigned to the proton. As shown in Fig. 2a, b, the 1H chemical shift did not change with increasing temperature. However, near 343 K, the chemical shift abruptly changed to a lower value of 8.3 ppm, which means that the structural geometry of 1H in KH3(SeO3)2 has changed. The chemical shift below T C (=211 K) splits into two lines, as shown in Fig. 2a, b. A doubling of the number of lines occurred in the low temperature phase; the line for the 1H nucleus below 211 K consisted of two resonance signals, δ = 11.3 ppm and δ = 12.9 ppm. The splitting of the chemical shift at 211 K supports the ferroelastic property previously reported [27].

Fig. 2
figure 2

a In situ 1H MAS NMR spectrum of KH3(SeO3)2 as a function of temperature and b chemical shift of 1H MAS NMR in KH3(SeO3)2 as a function of temperature

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For the protons in KH3(SeO3)2, the spin–lattice relaxation times in the rotating frame T 1ρ were measured at several temperatures. The nuclear magnetization decay of the protons can be described by the following single exponential function [31]: M(t) = M oexp(−t/T 1ρ ), where M(t) is the magnetization at the length of spin-locking pulse and Mo is the total nuclear magnetization of 1H at thermal equilibrium. The temperature dependence of the 1H spin–lattice relaxation time in the rotating frame T 1ρ is shown in Fig. 3. The proton T 1ρ data do not show any evidence of anomalous change near T C. The two T 1ρ values between the red circles and the black squares in Fig. 3 at low temperature were nearly same by ferroelastic property. Near the melting temperature, the T 1ρ of 1H decreased abruptly, and T 1ρ had very short values.

Fig. 3
figure 3

Spin–lattice relaxation time in the rotating frame T 1ρ of 1H in KH3(SeO3)2 as a function of temperature

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A structural analysis of 2H in deuterated KD3(SeO3)2 was conducted using 2H MAS NMR. The chemical shifts for 2H in KD3(SeO3)2 were measured as a function of temperature, as shown in Fig. 4. The spectrum exhibited one peak at δ = 9.5 ppm with respect to tetramethylsilane (TMS); this signal at a chemical shift of 9.5 ppm was assigned to 2H, and was almost independent of temperature. At the transition point near T C (=302 K), the 2H NMR chemical shift was continuous. This means that the structural geometry of 2H in KD3(SeO3)2 did not change near the phase temperature. The chemical shift near the melting temperature changed abruptly to δ = 3.2 ppm. This is consistent with the chemical shift of 1H near T m in KH3(SeO3)2 shown in Fig. 2b.

Fig. 4
figure 4

Chemical shift of 2H MAS NMR in KD3(SeO3)2 as a function of temperature

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The decay traces of the magnetizations at 300 K were obtained from the MAS NMR signals of the 2H nuclei in the KD3(SeO3)2 crystals as shown in the inset in Fig. 5, for delay times ranging from 0.01 to 50 ms. Here, the asterisks are the spinning sidebands. The decay traces for 2H varied with the length of spin-locking pulse, and can be represented by fitting to a single exponential form. The spin–lattice relaxation time in the rotating frame for 2H in KD3(SeO3)2 was obtained as a function of temperature, as shown in Fig. 5. Here, the T 1ρ values were obtained from either the peak intensity or the area under the intensity curves for the 2H MAS NMR signal; the results obtained by the two methods are similar. The relaxation times of the 2H nuclei did not undergo anomalous changes near T C, but the T 1ρ values were smaller than below T C. Near the melting temperature, the T 1ρ of 2H had very short values. Their temperature dependences were similar to those of 1H in KH3(SeO3)2.

Fig. 5
figure 5

Spin–lattice relaxation time in the rotating frame T 1ρ of 2H in KD3(SeO3)2 as a function of temperature (filled squares T 1ρ obtained from peak intensity and filled circles T 1ρ obtained from the area under the curves) (inset the recovery behavior of the 2H MAS NMR signals at 300 K)

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5 Discussion and Conclusion

As protons are expected to play a dominant role in the physical properties and phase transition mechanisms of hydrogen-bonded crystals, probing the crystals deuterium motions with 2H NMR is expected to be a powerful means of studying their microscopic nature. The structural geometry near T C was studied by observing the chemical shifts and T 1ρ values of 1H and 2H using the MAS NMR method. In previous static solid-state NMR experiments on a single-crystalline sample, we observed a splitting of the 1H NMR line. To distinguish between different isotropic chemical shifts and magnetic inequivalence, we measured the 1H MAS NMR spectra. Since we observe only a single line, we can conclude that the differences between the two kinds of hydrogen bonds are due to magnetic inequivalence rather than chemical inequivalence.

The NMR relaxation times of 1H and 2H in KH3(SeO3)2 and KD3(SeO3)2 were measured in the rotating frame as a function of temperature. There were no significant changes in T 1ρ for 1H and 2H at T C, except for changes in the number of proton signals. The two resonance lines below 211 K were ascribed to the ferroelastic twin structure reported by Ivanov et al. [19]. The ferroelastic phase with twin domain structures below T C was transformed to the paraelastic phase with a single domain structure above T C. The twin structure appeared below the transition temperature T C; the number of lines observed below T C was twice the number observed above T C.

We compare these NMR results for the KH3(SeO3)2 and KD3(SeO3)2 obtained by MAS NMR in the rotating frame with NMR results obtained by static NMR in the laboratory frame previously reported [25, 26]. According to neutron diffraction study, hydrogen-bond lengths for KH3(SeO3)2 were different from those for KD3(SeO3)2 [29, 30]. Consequently, when a hydrogen was replaced by a deuterium, the spectra exhibit strong differences in the chemical shift of the proton and deuteron with an isotope effect of several ppm. The reason of this isotope effect may be due to the hydrogen-bond strength. However, in the case of the laboratory frame and the rotating frame, there are no significant changes in T 1 and T 1ρ for 1H and 2H at T C, respectively, and the role of structural changes in this transition is indeed relatively minor. And, the molecular motions in kHz range by MAS NMR in the rotating frame here obtained and those in MHz range by static NMR in the laboratory frame previously reported [25, 26] are very similar. The effects of deuteration of KH3(SeO3)2 include not only a shift in the phase transition temperature T C, but also a change in the local symmetry.