Ferroelastic property of tetramethylammonium tetrachlorozincate tetrachlorocuprate, [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1)

Abstract

The various crystallographic structures of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) may be understood by considering the different chemical shifts observed in ¹H MAS and ¹³C CP/MAS NMR spectra. Cu²⁺ ions, after replacing partially the Zn²⁺ ions, occupy the same locations in the lattice as the Zn²⁺ ions. The NMR spectrum and T_1ρ of x = 0.1 and 0.3 were found to be similar to those of pure [N(CH₃)₄]₂ZnCl₄, whereas the NMR spectrum and T_1ρ of x = 0.5 were different. Consequently, the existence of ferroelastic properties of N(CH₃)₄ ions in x = 0, 0.1, 0.3, and 1 are apparent at low temperatures, whereas they disappear for x = 0.5. It has been demonstrated that the replacement of Zn²⁺ ions with high concentrations of Cu²⁺ ions changes the ferroelastic property of the crystal.

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I. Introduction

Crystals of the formula A₂BX₄ have received a great deal of attention owing to their interesting phase transition sequences. [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ single crystals are A₂BX₄-type crystals. Tetramethylammonium tetrachlorozincate, [N(CH₃)₄]₂ZnCl₄, undergoes five phase transitions at the following temperatures: 161 K (T_C5), 181 K (T_C4), 276.3 K (T_C3), 279 K (T_C2), and 296 K (T_C1).^1–7 These previous studies have concluded that there are six phases, I to VI in the order of decreasing temperature, of [N(CH₃)₄]₂ZnCl₄ crystals. The crystal structure of phase I is orthorhombic. The transition from the normal (I) to the incommensurate (II) phase occurs at 296 K. The corresponding symmetry changes are as follows: the ferroelectric phase III is orthorhombic with space group P2₁cn; the ferroelastic phase IV is monoclinic with space group P2₁/n; the ferroelastic phase V is monoclinic with space group P2₁/c; and finally, phase VI is orthorhombic with space group P2₁2₁2₁.⁵ Furthermore, tetramethylammonium tetrachlorocuprate, [N(CH₃)₄]₂CuCl₄, crystals exhibit four phases, I to IV, with transition temperatures of 263 K (T_C3), 291 K (T_C2), and 301 K (T_C1).⁸ The structure and space group of the lowest temperature phase IV is monoclinic with space group P112₁/n. The structure of phase III is monoclinic with space group P12₁/c1, and phase II is incommensurate. The highest temperature phase, phase I, has an orthorhombic structure with space group Pmcn. These three phase transitions in [N(CH₃)₄]₂CuCl₄ are, in the order of increasing temperature: ferroelastic (IV)–ferroelastic (III), ferroelastic (III)–incommensurate (II), and incommensurate (II)–commensurate (I).⁹ In particular, these two compounds, [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄, have the ferroelastic property at low temperatures.

Ferroelasticity was first recognized as a structure property by Aizu in 1970.¹⁰ A crystal is ferroelastic if it has two or more stable orientation states in the absence of mechanical stress, and can be reversibly transformed from one to another of these states by the application of mechanical stress. When a ferroelastic crystal is heated, the ferroelastic effect usually disappears at a well-defined temperature. At this temperature, a structural phase transition occurs between a ferroelastic and a paraelastic phase; the main feature of which is that a ferroelastic hysteresis exists in one phase but not in the other. Also, the ferroelastic domain occurs in all ferroelastic crystals as a consequence of the reduction in symmetry between the paraelastic and ferroelastic phases.

The physical properties of [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ have been studied using various experimental methods by several research groups.^11–20 Ribet et al.²¹ reported observing ferroelectric–ferroelastic phase transitions of [N(CH₃)₄]₂ZnCl₄ through X-ray and synchrotron topography. Recently, the roles of chemically inequivalent a-N(CH₃)₄ and b-N(CH₃)₄ ions in [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ have been reported by static nuclear magnetic resonance (NMR) and magic angle spinning (MAS) NMR, respectively.^22,23 Furthermore, the ferroelastic phase transition of [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ at low temperatures have been discussed.²⁴

In this work, [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) single crystals were grown from aqueous solutions by the slow evaporation method. We measured the temperature dependences for ¹H magic angle spinning (MAS) NMR spectrum and ¹³C cross-polarization (CP)/MAS NMR spectrum of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ to elucidate the structural geometry. In addition, we determined the spin–lattice relaxation times in the rotating frame, T_1ρ, for ¹H and ¹³C nuclei in [N(CH₃)₄]₂Zn_1−xCu_xCl₄, for varying amounts of impurity Cu²⁺ ions. This is the first time that the local structures of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ have been investigated, and we used the results to analyze the role of N(CH₃)₄ ions. These results enabled us to compare the structural properties of pure [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄, and examine the effect of substituting Zn²⁺ ions in [N(CH₃)₄]₂ZnCl₄ with Cu²⁺ ions, with a focus on the effects of such substitution on ferroelasticity. Furthermore, in order to confirm the ferroelastic properties, domain structures were observed using an optical polarizing microscope.

II. Crystal structure

At room temperature, the [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ crystal is an orthorhombic system (space group P2₁cn) with Z = 4 and the following unit cell dimensions: a = 8.988 Å, b = 15.527 Å, and c = 12.269 Å.²⁵ The atomic arrangement in [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ consists of alternate organic–inorganic layers of a-N(CH₃)₄/Zn(Cu)Cl₄ and organic sheets b-N(CH₃)₄, both parallel to b-plane (Fig. 1).²⁶ This figure shows chains that are repeated sequences of Cu(Zn)Cl₄ and a-N(CH₃)₄, where the sense of tetrahedron orientation alternates within the same chain. The b-N(CH₃)₄ tetrahedra are present between the chains and on both sides of the organic–inorganic layers, building organic layers.

Fig. 1 The structure of [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ in the ab-plane. Cu/ZnCl₄²⁻ anions are represented by grey tetrahedrons. N(CH₃)₄⁺ cations are represented by empty tetrahedrons. The dashed boundaries show the development of the zigzag chain in the organic–inorganic layer along the [110] direction.

A [N(CH₃)₄]₂ZnCl₄ crystal in phase I has an orthorhombic structure with space group Pmcn. Its orthorhombic lattice constants are: a = 8.946 Å, b = 15.515 Å, and c = 12.268 Å.^27,28 In this phase, a unit cell contains Z = 4 units consisting of two inequivalent kinds of tetramethylammonium ions, hereafter abbreviated as a-N(CH₃)₄ and b-N(CH₃)₄, and one kind of ZnCl₄²⁻ ion.²⁷ The ZnCl₄ ion and the a-N(CH₃)₄ are positioned in a strongly correlated manner, while the b-N(CH₃)₄ is less correlated than the other kind of ions. Moreover, a [N(CH₃)₄]₂CuCl₄ crystal in phase I has an orthorhombic structure, and its orthorhombic lattice constants are: a = 9.039 Å, b = 15.515 Å, and c = 12.268 Å, which are slightly different from those for the hexagonal form.^29,30 In this phase, a unit cell contains Z = 4 units consisting of two inequivalent kinds of tetramethylammonium ions, as well as [N(CH₃)₄]₂ZnCl₄.

III. Experimental method

[N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) single crystals were grown at room temperature by slow evaporation of an aqueous solution containing ZnCl₂, CuCl₂, and N(CH₃)₄Cl, in stoichiometric proportions. [N(CH₃)₄]₂Zn_1−xCu_xCl₄ single crystals varied in color according to the amount of Cu²⁺ ions, as shown in Fig. 2.

Fig. 2 The colors of mixed crystals [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1).

Solid-state NMR experiments were performed using a Bruker DSX 400 FT NMR spectrometer at the Korea Basic Science Institute. ¹H MAS NMR and ¹³C CP/MAS NMR experiments were performed at the Larmor frequencies of 400.12 MHz and 100.61 MHz, respectively. The samples were placed in the 4 mm CP/MAS probe as powders. The MAS rate was set to 10 kHz and 7 kHz for ¹H MAS and ¹³C CP/MAS, respectively, to minimize the spinning sideband overlap. Here, the frequency scale of the spectrum for ¹H and ¹³C was expressed with respect to tetramethylsilane (TMS). In the case for ¹H, the T_1ρ measurements were performed using π/2–t–acquisition. The spin–lattice relaxation times in the rotating frame, T_1ρ, were measured by varying the length of the spin-locking pulses. The π/2 pulse width used for T_1ρ was 5 μs, corresponding to the frequency of the spin-locking field, 50 kHz. Moreover, the T_1ρ for ¹³C was obtained using CP–t–acquisition, and the frequency of the spin-locking field was 78.1 kHz. The experimental temperatures were maintained at constant values, with an accuracy of ±0.5 K, by controlling the nitrogen gas flow and heater current. The temperature-dependent NMR measurements were carried out in the temperature range from 150 to 450 K.

IV. Experimental results and analysis

At room temperature, the structures of the [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) crystals were determined with an X-ray diffraction system (Bruker AXS GMBH) at the Korea Basic Science Institute. The single crystals were mounted on a Bruker SMART CCD diffractometer equipped with a graphite-monochromated Mo Kα (λ = 0.71073 Å) radiation source. Data collection and integration were performed at 298 K with SMART (Bruker, 2000) and SAINT-Plus (Bruker, 2001).³¹ The lattice constants of the five crystals were shown in Table 1, and all the [N(CH₃)₄]₂Zn_1−xCu_xCl₄ crystals containing Cu²⁺ impurities had the same orthorhombic structure as [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄. And, the chemical composition of the crystals was confirmed with an electron probe microanalyzer (EPMA 1600). The X-ray diffraction and elemental analysis data indicate that these single crystals are [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0.1, 0.3, and 0.5). In addition, in order to determine the phase transition temperatures, differential scanning calorimetry (DSC) was carried out on the crystals with a Dupont 2010 DSC instrument. The measurements were performed at a heating rate of 10 °C min⁻¹ in the temperature range from 200 K to 500 K, and the endothermic peaks for x = 0.1, 0.3, and 0.5 were shown in Fig. 3. The phase transition temperatures are nearly unchanged with varying amounts of impurity Cu²⁺ ions and are similar to those for pure [N(CH₃)₄]₂ZnCl₄.

Table 1 The lattice constants of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) at room temperature

	a	b	c
[N(CH3)4]2ZnCl4 (x = 0)	8.9958 ± 0.0030	15.5162 ± 0.0039	12.2517 ± 0.0034
[N(CH3)4]2Zn0.9Cu0.1Cl4 (x = 0.1)	8.9994 ± 0.0027	15.5164 ± 0.0037	12.2713 ± 0.0029
[N(CH3)4]2Zn0.7Cu0.3Cl4 (x = 0.3)	8.9988 ± 0.0020	15.5388 ± 0.0035	12.2663 ± 0.0035
[N(CH3)4]2Zn0.5Cu0.5Cl4 (x = 0.5)	9.0068 ± 0.0027	15.5409 ± 0.0043	12.2774 ± 0.0032
[N(CH3)4]2CuCl4 (x = 1)	9.1136 ± 0.0029	15.2723 ± 0.0046	12.1526 ± 0.0050

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Fig. 3 Differential scanning calorimetry (DSC) thermogram of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0.1, 0.3, and 0.5) single crystals.

A. ¹H MAS NMR in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1)

Structural analysis of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) was carried out with the ¹H MAS NMR method. The chemical shifts for ¹H in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5) were measured over the temperature range of 180–425 K, as shown in Fig. 4(a). In the cases of x = 0, 0.1, 0.3, and 0.5, the small changes in the chemical shifts near 296 K correspond to phase transitions. The chemical shift of [N(CH₃)₄]₂Zn_0.9Cu_0.1Cl₄ with x = 0.1 changes near 276 K, meaning structural phase transition. However, the other phase transitions cannot be identified from the chemical shifts. Alternatively, the insert in Fig. 4(b) shows the ¹H MAS NMR spectrum of [N(CH₃)₄]₂CuCl₄ with x = 1 at room temperature. The NMR spectrum consists of two peaks at chemical shifts of 2.45 and 6.80 ppm. The spinning sidebands are marked with asterisks. The signals at chemical shifts of 2.45 and 6.80 ppm are assigned to the methyl protons, and they are clearly due to magnetically inequivalent sites. Here, the two proton peaks at 2.45 and 6.80 ppm cannot be distinguished between a-N(CH₃)₄ or b-N(CH₃)₄. The ¹H chemical shift changes with increasing temperature, as shown in Fig. 4(b). The chemical shifts near T_C3 also change abruptly, whereas those near T_C1 and T_C2 change almost continuously. The chemical shift in the case for x = 1 is completely different from those for x = 0, 0.1, 0.3, and 0.5. This difference is due to variations in the electronic structure of the Zn²⁺ and Cu²⁺ ions.

Fig. 4 (a) Chemical shifts of the ¹H MAS NMR spectrum as a function of temperature in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5) and (b) chemical shift of the ¹H MAS NMR spectrum as a function of temperature in [N(CH₃)₄]₂CuCl₄ (x = 1) (inset: ¹H MAS NMR spectrum for [N(CH₃)₄]₂CuCl₄ at room temperature).

The spin–lattice relaxation times in the rotating frame, T_1ρ, for the proton in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.3, 0.5, and 1) were obtained as a function of temperature. The nuclear magnetization recovery curves obtained for protons were described by the following single exponential function:^32–34 S(t) = S₀ exp(−t/T_1ρ), where S(t) is the magnetization at time, t, and S₀ is the total nuclear magnetization of ¹H at thermal equilibrium. The slopes of the recovery traces are different at each temperature. The temperature dependences of the ¹H T_1ρ are shown in Fig. 5. When the paramagnetic Cu²⁺ impurity was included, x = 0.3 in [N(CH₃)₄]₂Zn_1−xCu_xCl₄, the trend in T_1ρ resembles that of ¹H T_1ρ in pure [N(CH₃)₄]₂ZnCl₄. Below T_C3, T_1ρ increases abruptly, and the proton T_1ρ data does not show any evidence of an anomalous change near the phase transition temperatures of T_C1 and T_C2. However, the ¹H T_1ρ curve of [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ is markedly different from those observed for pure [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄. Here, the ¹H T_1ρ values for [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ are smaller than those in [N(CH₃)₄]₂ZnCl₄, and larger than that in [N(CH₃)₄]₂CuCl₄. In the case for [N(CH₃)₄]₂CuCl₄ with x = 1, the ¹H T_1ρ was found to be much shorter than that for [N(CH₃)₄]₂ZnCl₄. The T_1ρ values increase with increasing temperature and the change is discontinuous near T_C3, but relatively continuous near T_C1 and T_C2.

Fig. 5 Temperature dependences of the ¹H spin–lattice relaxation time in the rotating frame, T_1ρ, in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.3, and 0.5). (Inset: temperature dependences of the ¹H spin–lattice relaxation time in the rotating frame, T_1ρ, in [N(CH₃)₄]₂CuCl₄.)

B. ¹³C CP/MAS NMR in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1)

Structural analysis of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) was carried out using ¹³C NMR spectroscopy. The chemical shifts for ¹³C in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5) were measured over the temperature range of 170–430 K, as shown in Fig. 6(a). In the cases for x = 0, 0.1, 0.3, and 0.5, the ¹³C CP/MAS NMR spectrum in the temperature range 293–380 K consists of a single resonance line for one type of N(CH₃)₄, as shown in Fig. 6(a). The chemical shifts of CH₃ in the two inequivalent kinds of a-N(CH₃)₄ and b-N(CH₃)₄ in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5) were not measured within this temperature range. In the case for [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, and 0.3), the ¹³C NMR chemical shift at the transition point of 276 K (=T_C3) splits into two lines, as shown in Fig. 6(a). This splitting indicates that at this temperature there is a phase transition to a new phase with a monoclinic symmetry lower than the orthorhombic symmetry. The III–IV transition results in an abrupt splitting of the ¹³C NMR line into two components, indicative of a ferroelastic property. The ferroelastic domain structures in phase IV of [N(CH₃)₄]₂ZnCl₄ (x = 0) and [N(CH₃)₄]₂Zn_0.7Cu_0.3Cl₄ (x = 0.3) were confirmed by employing an optical polarizing microscope. Fig. 6(c) shows the domain patterns for the ferroelastic and paraelastic phases of x = 0 and x = 0.3. The domain patterns at 350 K do not appear similar to those for the paraelectric phase. The appearance of microscope domain walls with many parallel lines with decreasing temperature is a property of the ferroelastic phase. In the case for [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ (x = 0.5), the ¹³C NMR spectrum at all temperatures measured here consists of only one resonance line, as shown in Fig. 6(a). The in situ ¹³C CP/MAS NMR spectrum for [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ are also shown in Fig. 6(b) as a function of temperature. Furthermore, there were only continuous quantitative changes in the chemical shift, where the ¹³C chemical shift slowly and monotonically increases with temperature. In the case for [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ with x = 0.5 the domain walls did not appear at all temperatures, as shown in Fig. 6(c).

Fig. 6 (a) Chemical shifts of the ¹³C CP/MAS NMR spectrum as a function of temperature in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5), (b) in situ ¹³C CP/MAS NMR spectrum as a function of temperature in [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄, and (c) domain wall patterns of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.3, and 0.5) at 250 K and 350 K obtained with optical polarizing microscopy.

On the other hand, the ¹³C CP/MAS NMR spectrum for [N(CH₃)₄]₂CuCl₄ at room temperature has two signals at chemical shifts of δ = 72.13 and 133.48 ppm. The signals at chemical shifts of δ = 72.13 and 133.48 ppm represent the methyl carbons in inequivalent b-N(CH₃)₄ and a-N(CH₃)₄, respectively. In the X-ray diffraction study of Hasebe et al.,²⁷ the deformation of the b-N(CH₃)₄ ion was larger than that for the a-N(CH₃)₄ ion, and the degree of the deformation was enlarged in the ferroelectric phase. Based on these results, a-N(CH₃)₄ and b-N(CH₃)₄ are defined according the change of the relaxation time as a function of temperature, which is discussed next. Fig. 7(a) shows the ¹³C CP/MAS NMR spectrum below 291 K, in which the ¹³C chemical shifts are shown by the three lines. Above T_C2 (291 K), the ¹³C NMR spectrum consists of two lines for a-N(CH₃)₄ and b-N(CH₃)₄, as shown in Fig. 7(a). However, at the transition point at 291 K, the ¹³C NMR chemical shifts split into three lines. This splitting indicates that there is a phase transition at this temperature to a new phase with monoclinic symmetry, which is a symmetry reduction from orthorhombic symmetry. Thus, the II–III transition results in an abrupt splitting of the ¹³C NMR line into three components, which is indicative of ferroelasticity. Furthermore, above 291 K, there were only continuous quantitative changes in the chemical shift, where the ¹³C chemical shift slowly and monotonically decreases with increasing temperature. The ferroelastic domain structures in phases III and IV of [N(CH₃)₄]₂CuCl₄ with x = 1 were observed by employing an optical polarizing microscope, as shown in Fig. 7(b). The domain walls in the ferroelastic phase of phase IV were measured, whereas those in the paraelastic phase of phase I had disappeared. Consequently, the NMR spectrum and domain walls of [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 1) below 276 K show the ferroelastic characteristic, whereas the NMR spectrum and domain patterns of [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ below 276 K do not.

Fig. 7 (a) Chemical shift of the ¹³C CP/MAS NMR spectrum as a function of temperature in [N(CH₃)₄]₂CuCl₄ (x = 1) and (b) domain wall patterns of [N(CH₃)₄]₂CuCl₄ at 250 K and 350 K obtained with optical polarizing microscopy.

The spin–lattice relaxation times in the rotating frame, T_1ρ, in the [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.3, 0.5, and 1) were obtained for each carbon as a function of temperature, with variable spin locks on the carbon channel following cross-polarization. The ¹³C magnetization was generated by cross-polarization, after spin locking of the protons. The proton field was then turned off for a variable time, t, while the ¹³C rf field remained on. Finally, the ¹³C free induction decay was observed under high-power proton decoupling, and a Fourier transform was subsequently applied. Values of T_1ρ could be selected by the Fourier transformation of the free-induction decay (FID), after spin locking and repetition of the experiment with variations in the time, t. The signals obtained for carbon were described by a single exponential function. Fig. 8(a) shows the T_1ρ values for ¹³C in the cases of x = 0, 0.3, and 0.5. The slopes of the T_1ρ values near 296 K (=T_C1) are different, and this temperature corresponds to phase transition. The T_1ρ values for two ¹³C signals in the ferroelastic phase are nearly the same within the experimental error range. In the case for [N(CH₃)₄]₂CuCl₄ with x = 1, the ¹³C T_1ρ values for a-N(CH₃)₄ and b-N(CH₃)₄, shown in Fig. 8(b), are similar, especially at higher temperatures. However, near T_C3, the T_1ρ values change abruptly, and the T_1ρ values for the two ¹³C signals of b-N(CH₃)₄, produced by the ferroelastic twin structure below T_C2, are the same within the experimental error range.

Fig. 8 (a) Temperature dependences of the ¹³C spin–lattice relaxation time in the rotating frame, T_1ρ, in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.3, and 0.5) and (b) temperature dependences of the ¹³C T_1ρ in [N(CH₃)₄]₂CuCl₄.

V. Discussion

The structures and the phase transition temperatures of the mixed crystals [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) were determined with X-ray diffraction and DSC, respectively. Here, the structure or phase transition temperatures were almost unchanged by the doping of [N(CH₃)₄]₂ZnCl₄ crystals with Cu²⁺ ions.

The chemical shifts for ¹H and ¹³C nuclei in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ were studied as a function of temperature. The chemical shifts in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ varied according to the concentration of Cu²⁺ ions. The differences in the chemical shifts among the members of the series could potentially be due to differences in the electron structures of Zn²⁺ and Cu²⁺, in particular, the structure of the d electrons, which screen the nuclear charge from the motion of the outer electrons. Zn²⁺ has a filled d shell, whereas Cu²⁺ has one s electron outside the closed d shell.

[N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄ contains two inequivalent types of N(CH₃)₄ ions, a-N(CH₃)₄ and b-N(CH₃)₄, respectively. Here, the two inequivalent kinds of a-N(CH₃)₄ and b-N(CH₃)₄ in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 0.5) were not measured. However, the two crystallographically different ions a-N(CH₃)₄ and b-N(CH₃)₄ in [N(CH₃)₄]₂CuCl₄ were identified using ¹³C CP/MAS NMR. However, the ¹H and ¹³C T_1ρ values were obtained with varying concentrations of Cu²⁺ ions in [N(CH₃)₄]₂Zn_1−xCu_xCl₄. It is apparent that T_1ρ for ¹H and ¹³C are not governed by the same mechanism for the amount of paramagnetic impurity Cu²⁺. As a result, the trends in the NMR spectrum and T_1ρ of ¹H and ¹³C nuclei in the [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0.1 and 0.3) were similar to those for [N(CH₃)₄]₂ZnCl₄. However, the structural properties of [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄ were strongly affected.

The T_1ρ values of materials including paramagnetic ions are smaller than those of pure [N(CH₃)₄]₂ZnCl₄. Because T_1ρ should be inversely proportional to the concentration and to the square of the magnetic moment of the paramagnetic ions, the T_1ρ values for samples containing paramagnetic ions are generally smaller than for those without. Therefore, T_1ρ for ¹H and ¹³C are driven in these systems by the fluctuations of the magnetic dipole of the Cu²⁺ paramagnetic ions.

VI. Conclusion

The purpose of this study was to investigate how the local structure in a pure crystal is affected by the random presence of a cation of a different size, and to determine the influence of this substitution on the physical properties of the crystal. After the partial replacement of Zn²⁺ ions by Cu²⁺ ions, the Cu²⁺ ions occupied the same locations in the lattice as the Zn²⁺ ions did. Their crystallographic structures in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, 0.5, and 1) can be understood by considering the differences in the chemical shifts of the ¹H MAS NMR and ¹³C CP/MAS NMR spectra. The NMR spectrum and T_1ρ for x = 0.1 and 0.3 were similar to those for pure [N(CH₃)₄]₂ZnCl₄, whereas the NMR spectrum and T_1ρ for x = 0.5 were different.

The variation of the structural geometry, as a function of impurity concentration in the mixed system, was interpreted in terms of the differences in size and electron structure between the host and impurity ions. In particular, we attempted to explain the role of CH₃ in the spin–lattice relaxation time mechanisms for the systems containing the paramagnetic Cu²⁺ impurity, based on the ¹H MAS NMR and ¹³C CP/MAS NMR data in [N(CH₃)₄]₂ZnCl₄ and [N(CH₃)₄]₂CuCl₄. Consequently, the existence of ferroelastic properties of N(CH₃)₄ ions in [N(CH₃)₄]₂Zn_1−xCu_xCl₄ (x = 0, 0.1, 0.3, and 1) were apparent at low temperatures, whereas they were absent for [N(CH₃)₄]₂Zn_0.5Cu_0.5Cl₄. This study has shown that the replacement of Zn²⁺ ions with a high concentration of Cu²⁺ ions causes the ferroelastic property of the structure to disappear.

Acknowledgements

This research was supported by the Basic Science Research program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2012001763).

References

1. J. D. Axe, Incommensurate phases in Dielectrics, ed. R. Blinc and A. P. Levanyuk, North-Holland, Amsterdam, 1986.
2. H. Z. Cummins, Phys. Rep., 1990, 185, 211.
3. I. R. Larrea, A. Lopez Echarri and M. J. Tello, J. Phys. C: Solid State Phys., 1981, 14, 3171.
4. M. Hohioka, J. Phys. Soc. Jpn., 1983, 52, 4056.
5. S. Sawada, I. Yamaguchi, H. Suzuki and F. Shimizu, J. Phys. Soc. Jpn., 1985, 54, 3129.
6. K. Parlinski and F. Denoyer, J. Phys. C: Solid State Phys., 1985, 18, 293.
7. G. Madariaga, F. J. Zuniga, J. M. Perez-Mato and M. J. Tello, Acta Crystallogr., Sect. B: Struct. Sci., 1987, 43, 356.
8. B. Martin, J. M. Pastar, F. Rull and J. A. De Saja, Solid State Commun., 1982, 44, 1047.
9. A. G. Cuevas, M. J. Tello, J. Fernandez, A. L. Echarri, J. Herreros and M. Couzi, J. Phys. C: Solid State Phys., 1983, 16, 473.
10. K. Aizu, Phys. Rev. B: Solid State, 1970, 2, 754.
11. A. A. El Fadl, A. El-Korashy and H. El-Zahed, J. Phys. Chem. Solids, 2002, 63, 375.
12. A. El-Korashy, J. Mater. Sci. Lett., 2000, 19, 29.
13. V. B. Kapustyanyk and A. Y. Batyuk, J. Appl. Spectrosc., 2004, 71, 387.
14. S. A. Sveleba, I. V. Karpa, I. M. Katerynchuk, O. V. Semotyuk, R. M. Shymkiv, I. M. Kunyo and O. I. Fitsych, J. Appl. Spectrosc., 2011, 78, 228.
15. D. G. Sannikov, Phys. Solid State, 2005, 47, 324.
16. D. G. Sannikov and G. A. Kessenikh, Phys. Solid State, 2005, 47, 729.
17. D. G. Sannikov, Phys. Solid State, 2000, 42, 2282.
18. A. Y. Batyuk, V. B. Kapustyanyk and Y. M. Korchak, J. Appl. Spectrosc., 2005, 72, 413.
19. R. M. Shymkiv, S. A. Sveleba, I. V. Karpa, I. N. Katerynchuk, I. M. Kunyo and E. I. Phitsych, J. Appl. Spectrosc., 2011, 78, 823.
20. A. El-Korashy and M. G. Brik, Solid State Commun., 2005, 135, 298.
21. M. Ribet, S. Leon, F. Lefaucheux and M. C. Robert, J. Appl. Crystallogr., 1990, 23, 277.
22. A. R. Lim and K.-Y. Lim, Solid State Sci., 2014, 31, 70.
23. A. R. Lim, J. Mol. Struct., 2014, 1056–1057, 233.
24. A. R. Lim, D. K. Park, J.-H. Chang and S.-Y. Jeong, J. Phys. Soc. Jpn., 2001, 70, 1937.
25. A. B. Rhaiem, F. Hiel, K. Geidara and M. Gargouri, Spectrochim. Acta, Part A, 2007, 66, 1107.
26. F. Hlel, A. B. Rhaiem and K. Guidara, Russ. J. Inorg. Chem., 2008, 53, 785.
27. K. Hasebe, H. Mashiyama, N. Koshiji and S. Tanisaki, J. Phys. Soc. Jpn., 1987, 56, 3543.
28. F. J. Zuniga, G. Madariaga and J. M. Perez-Mato, Acta Crystallogr., Sect. B: Struct. Sci., 1989, 45, 462.
29. W. Rehwald and A. Vonlanthen, Z. Phys. B: Condens. Matter, 1985, 61, 25.
30. K. Gesi and M. Iizumi, J. Phys. Soc. Jpn., 1980, 48, 1775.
31. SMART and SAINT-Plus v6.22, Bruker AXS Inc., Madison, Wisconsin, USA, 2000.
32. J. L. Koenig, Spectroscopy of Polymers, Elsevier, New York, 1999.
33. B. Cowan, Nuclear Magnetic Resonance and Relaxation, Cambridge Univ., UK, 1997.
34. N. Bloembergen, E. M. Purcell and R. V. Pound, Phys. Rev., 1948, 73, 679.

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