Introduction

Crystals of solid solutions of Csx(NH4)1−xLiSO4 belong to the family of double sulfates with general formula being ALiSO4, where: A = (Cs, NH4, Rb, K, Na). The crystalline structure of these compounds may be considered as a small distortion of the prototype structure α-K2SO4 with P63/mmc symmetry [1]. For majority of compounds, this phase is not observed experimentally. However, the most widespread low-temperature implementation of the α-K2SO4 lattice is the β-K2SO4 structure which is characterized by a lattice of a rhombic symmetry [2]. These compounds have a characteristic skeletal structure, which is a derivative of the tridymite structure. It consists of two types of tetrahedrons: LiO4 and SO4 [3].

During lowering the temperature, the β-K2SO4 crystalline modification very often loses its stability and as a result of a single phase transition or a sequence of transitions, the crystals transform into: ferroelectric, ferroelastic, or incommensurate phases. The variety of phases is also largely influenced by the “chemical” pressure which may be changed by the replacement of cations and anions in the β-K2SO4 structure [4].

The base crystals of the solid solution of Csx(NH4)1−xLiSO4: lithium cesium sulfate CsLiSO4 (LCS) and lithium ammonium sulfate β-NH4LiSO4 (LAS) crystallize at room temperature in the rhombic system [3, 5]. In these compounds, depending on the size of the A cation, the structural phase transition from the rhombic phase to the ferroleastic monoclinic phase takes place directly as it happens in case of the CsLiSO4 crystal [5–10] or via the ferroelectric phase as for the β-NH4LiSO4 crystal [4, 11–14].

The application of newly produced materials very often depends on possibilities of obtaining the desired properties at room temperature. This aim may be reached by obtaining solid solutions of base compounds, modifying not only the values of the structural phase transition temperature but also their properties. Due to a series of very interesting physical properties, including the ferroic properties, solid solutions of Csx(NH4)1−xLiSO4 became recently an object of intensively developed research.

Crystals of solid solutions of Csx(NH4)1−xLiSO4, where 0 ≤ x ≤ 1 were object of investigations with the use of optical and calorimetric methods [4, 15]. Areas of crystalline structures of various symmetries were identified based on the tests results. Suitable data were presented in the phase diagram x–T in Fig. 1. The extreme points of the diagram correspond, respectively, to the β-LAS (x = 0) and LCS (x = 1) compounds and for x = 0.4 the triple point is visible, where phases with Pmcn, P21cn, and P1121/n symmetries come together. Optical tests have shown that even a slight replacement of far larger Cs+ cations with \( N{\text{H}}_{4}^{ + } \) cations influences the optical properties of crystals and also the character of the phase transition; however, its ferroelastic nature remains unchanged. With growing content of the \( N{\text{H}}_{4}^{ + } \) ions concentration, the temperature of ferroelastic transition (for LCS T c = 202 K) increases, as well as the rotation angle of the optical indicatrix, whereas the transition remains continuous. For the concentration of x = 0.5, the monoclinic ferroelastic phase becomes visible at room temperature but its stability decreases—during cooling, another phase transition appears, as a result of which, at the temperature of 220 K, the crystal transforms from the monoclinic ferroelastic phase to a ferroelectric polar phase of rhombic symmetry.

Fig. 1
figure 1

Phase diagram x–T for the solid solution of Csx(NH4)1−xLiSO4, obtained in the heating process during DSC tests (unfilled circles); in the cooling process during optical tests (filled circles)— according to papers [15, 16]

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For x = 0.39, the monoclinic phase P1121 /n exists only in a very narrow range of temperatures of ca. 25 K. Birefringence examination for a concentration of x = 0.39 in the temperature range of 300÷350 K showed that the first transition is of a continuous nature, while the second phase transition is discontinuous with quite a high-temperature hysteresis (ΔT = 30 K). It was also found that for the range of cesium ions concentration of 0.35 < x ≤ 1, the ferroelastic phase P1121/n in Csx(NH4)1−xLiSO4 is present up to the temperature of liquid nitrogen. Calorimetric and optical tests (of optical double refraction) of solid solutions for the concentration scope x (x = 0; 0.045; 0.065; 0.09; 0.125; 0.15; 0.22) closer to the left, extreme point of the phase diagram have shown that the temperatures of both phase transitions in LAS (T 1LAS = 460.5 K (x = 0); 453 K (0.045); 449 K (0.065); 445 K (0.09); 431.5 K (0.15); 414.6 K (0.22) and T 2LAS = 289 K (x = 0); 280 K (0.045); 268.5 K (0.065); 260 K (0.09); 229, 241 K (0.15)) decrease significantly along with the increase of cesium concentration, the nature of the high-temperature transition remaining unchanged. It was noted that significantly larger influence of change of concentration x is observed for the temperature of the second phase transition; the area of the presence of the ferroelectric phase widens and for x = 0.22, the phase can be observed until the temperature reaches 77 K. A replacement of cations, \( N{\text{H}}_{4}^{ + } \) → Cs+, results in an abrupt increase of double refraction δ n and temperature hysteresis ΔT 2 in the phase transition from the ferroelectric phase P21cn to the ferroelastic phase P21/c11. Hence, for x = 0; 0.065; 0.15 the values of δ n and ΔT equal, respectively: δ n = 10·10−4, ΔT = 2 K; δ n = 12·10−4, ΔT = 8.5 K; δ n = 15·10−4, ΔT = 18 K [15].

Ferroic phase transitions in crystals from the family of double sulfates are connected with gradual ordering of the orientation of structural units SO4 and LiO4, with the leading role played by SO4 tetrahedrals [2, 5, 17]. Since isostructural compounds with an identical chemical formula, ALiSO4, show different sequences of ferroic phase transitions within quite a wide temperature range, research on their solid solutions has been taken [4, 15, 16, 18–20] in order to explain the subtle mechanisms determining the ordering processes in different compounds in this family. This paper is focused on the compounds of Csx(NH4)1−xLiSO4 for x = 0.90 and 0.85.

Technology of obtaining solid solutions of Cs0.90(NH4)0.10LiSO4 and Cs0.85(NH4)0.15LiSO4

The solid solutions of lithium cesium sulfate and lithium ammonium sulfate Csx(NH4)1−xLiSO4, where: x = 0.90, 0.85, were obtained as a result of slow evaporation of aqueous solutions of Cs2SO4, Li2SO4·H2O, and (NH4)2SO4 compounds, taken in appropriate stechiometric proportions. The above-mentioned crystals were grown at a temperature of 305.5 ± 0.2 K. In order to provide test with the electron paramagnetic resonance method, samples were doped with vanadyl ions by adding hydrated vanadyl sulfate VOSO4·5H2O in the amount of 1 % mole to the initial compounds. Solid solutions of Csx(NH4)1-xLiSO4 crystallize in the form of a pseudohexagonal prism, which consists of growth twins. In polarized light, for a section perpendicular to a pseudohexagonal axis c, attenuation is observed every 60 degrees; hence, the crystal is built of 6 growth twins. Figure 2 shows the view of the growth twins in the polarized light (a) and the morphology of a solid solution of Csx(NH4)1−xLiSO4, where: x = 0.85.

Fig. 2
figure 2

Crystal of the solid solution of Cs0.85(NH4)0.15LiSO4: a the view of growth twins in polarized light; b morphology of the crystal

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The ammonium ion content in the solid solutions (x = 0.90; 0.85) was determined using the Kjeldahl method [21] after making all non-destructive tests. For this purpose, a weighed sample was placed in a round-bottom flask being a part of the Parnas-Wagner apparatus. Next, a sodium hydroxide solution was added and ammonia was distilled off with steam into a receiver containing a standardized solution of sulfuric acid (VI). The excess of the acid was back-titrated with a standardized sodium hydroxide solution. It was found that the real ammonium ion concentration was twice lower than the one applied in the initial substances.

Research methodology

For the DSC tests, a Netzsch STA 409C analyzer was used with a controller which allows taking measurements within a wide temperature range: from the temperature of liquid nitrogen to 1,673 K, to an accuracy of ±0.1 K. The rate of heating (cooling) may vary within the range from 0.1 K min−1 to 20 K min−1. The measurements were performed in a controlled argon atmosphere.

For optical examinations, a polarizing microscope was used, Nikon Eclipse LV 100 POL, equipped with a heating and cooling system, THMS 600. Accuracy of temperature stabilization was ± 0.1 K.

Results and discussion

Figure 3 presents a DSC curve which was recorded for the solid solution of Cs0.90(NH4)0.10LiSO4 during the cooling process conducted at a rate of 1 K min−1.

Fig. 3
figure 3

DSC curve for the solid solution of Cs0.90(NH4)0.10LiSO4

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Analysis of the DSC curve for the solid solution of Cs0.90(NH4)0.10LiSO4 reveal two thermal anomalies for the temperatures: T p = 203.8 K and T p1 = 171.7 K, respectively. The anomaly that occurs at 203.8 K is connected with a structural ferroelastic phase transition (like in the case of crystal CsLiSO4 where the transition proceeds from the orthorhombic system to the monoclinic system). The values of parameters T o, T p, and T e for the thermal anomaly designated as (1) in Fig. 3 were calculated using the Proteus application [22]. They are presented in Table 1, where: T o, T p, and T e designate the temperature at the initial, extreme, and final points of the anomaly.

Table 1 Values of parameters T o, T p, and T e of the solid solution of Cs0.90(NH4)0.10LiSO4 for thermal anomaly (1)
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Figure 4 presents a DSC curve which was recorded for the solid solution of Cs0.85(NH4)0.15LiSO4 also during the cooling process conducted at a rate of 1 K/min.

Fig. 4
figure 4

DSC curve for the solid solution of Cs0.85(NH4)0.15LiSO4

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The dependence presented in Fig. 4 has two characteristic thermal anomalies at T p = 230.1 K and T p1 = 197.1 K. This seems to have some similarity with DSC curve for the sample of Cs0.90(NH4)0.10LiSO4.

The thermal anomaly at the temperature of 230.1 K testifies to an expected increase in the temperature of the structural ferroelastic phase transition in the process of substituting Cs+ cations with \( N{\text{H}}_{4}^{ + } \) cations. In addition, the values of parameters T o, T p, and T e were calculated for the thermal anomaly designated as (1) in Fig. 4, and presented in Table 2.

Table 2 Values of parameters T o, T p, and T e of the solid solution of Cs0.85(NH4)0.15LiSO4 for thermal anomaly (1)
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Due to the ferroelastic nature of the structural phase transition, expected in solid solutions, it can be presumed that a domain structure will become visible below the phase transition temperature. For this purpose, both crystals were examined using polarization microscopy. Figure 5 shows the forming of and temperature related changes in the ferroelastic domain structure of the solid solution crystal Cs0.85(NH4)0.15LiSO4 at selected temperatures.

Fig. 5
figure 5

Evolution of the domain structure in the crystal of solid solution Cs0.85(NH4)0.15 during the lowering of temperature: a 218 K, b 213 K, c 198 K along with a system of ferroelastic domains, S 1 and S 2, separated by two allowed, mutually perpendicular domain walls W a || (100) and W b || (010)

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In the high-temperature phase, growth twins are observed which are distinguished by different colors. (Fig. 2a). Equations of the planes constituting boundaries of the twinned areas are given by: x = 0, y = 0, \( y = \pm \sqrt 3 \,x \), \( y = \pm 1/\sqrt 3 \,x \) (determined in the system of hexagonal axes of the prototype phase P63/mmc). They satisfy the equations derived by Sapriel for domain walls [23] as well as the relationships imposed by the symmetry elements lost during the transformation which lead to a reduction of symmetry according to the scheme 6/mmm → mmm.

During the lowering of temperature of the solution Cs0.85(NH4)0.15LiSO4, the color of the twins observed in polarized light changes. The formation of a domain structure begins at temperature T c = 223 ± 2 K from the appearance of optically inhomogeneous regions. Since crystals from the ALiSO4 family belong, according to Aizu’s notation, to mmmF2/m [24]; in accordance with the change of the crystal symmetry during a structural phase transition, the ferroelastic domain structure is built of ferroelastic domains of two types, S 1 and S 2. The domains are separated by mutually perpendicular domain walls of two types, W a, b, parallel to axis a or b of the crystal, respectively; this is in accord with the theoretical equations [23] for ferroelastic domain walls: x = 0, y = 0 (in the rhombic system).

As can be seen in Fig. 5, close to a temperature of 213 K, the domain structure consists of a large number of domains in the form of narrow strips; the domains are separated with W b type walls of one family only (parallel to plane (010)). As the temperature further decreases, close to 198 K, the existence of domains in the form of narrow strips is still observed; however, these strips are separated with mutually perpendicular walls of W a || (100) and W b || (010) type. Also in the Cs0.90(NH4)0.10LiSO4 solution, the structural phase transition is observed through a similar system of ferroelastic domains which appear near the temperature of 205 K.

In the base crystal, CsLiSO4, the refinement of the domain structure is maintained within a very narrow range of temperatures (2 K below T c). Beyond these temperatures big domains are formed and are stable in terms of temperature [6, 25]. In both of the investigated crystals of the solid solution Csx(NH4)1−xLiSO4, a fine domain structure is maintained within a wide temperature range below the temperatures of their phase transitions.

Conclusions

Through slow evaporation of water solutions of the compounds: Cs2SO4, Li2SO4·H2O, and (NH4)2SO4 at temperature T = 305.5 K, two types of solid solutions of Csx(NH4)1−xLiSO4 were grown, where x = 0.90; 0.85. Using Kjeldahl method it was found that the real ammonium ion concentration is twice lower than the one applied in the initial substances, which testifies to the loss of ammonium ions during the crystallization process. The DSC examinations of the solid solutions of Csx(NH4)1−xLiSO4 with the content of x = 0.90 and 0.85 show that the temperature of the ferroelastic phase transition increases as the Cs+ ions get replaced with \( NH_{4}^{ + } \) ions. This temperature increases from 202 K for pure CsLiSO4 to the temperature of 203.8 K for Cs0.90(NH4)0.10LiSO4, and 230.1 K for Cs0.85(NH4)0.15LiSO. The formation of the ferroelastic domain structure in the solid solutions Cs0.85(NH4)0.15LiSO4, and Cs0.90(NH4)0.10LiSO4 is connected with the structural phase transition from the paraelastic to ferroelastic phase.