ISSN 0030-400X, Optics and Spectroscopy, 2018, Vol. 124, No. 2, pp. 216–220. © Pleiades Publishing, Ltd., 2018. Original Russian Text © V.I. Stadnyk, M.Ya. Rudish, P.A. Shchepansky, I.M. Matviishyn, V.M. Gaba, O.M. Gorina, 2018, published in Optika i Spektroskopiya, 2018, Vol. 124, No. 2, pp. 221–225.
CONDENSED-MATTER SPECTROSCOPY
The Effect of Uniaxial Pressures on the Infrared Spectra of LiNH4SO4 Crystals V. I. Stadnyka, *, M. Ya. Rudisha, b, P. A. Shchepanskya, b, I. M. Matviishyna, V. M. Gabac, and O. M. Gorinac a
b
Franko Lviv National University, Lviv, 79005 Ukraine Jan Dlugosz University in Czestochowa, Czestochowa, 42200 Poland c Lviv Polytechnic National University, Lviv, 79013 Ukraine *e-mail:
[email protected] Received October 3, 2017
Abstract—The infrared reflection spectra of mechanically free and uniaxially compressed LiNH4SO4 crystals are studied for the first time in the spectral range of 800–1700 сm–1 along three crystallophysical directions. The Kramers–Kronig dispersion relations are used to determine the dispersion and baric dependences of refractive index n and the real ε1 and imaginary ε2 parts of the dielectric constant and to calculate the frequencies of longitudinal ωLO and transverse ωТO vibrations, decay constant γ, and oscillator strength f of mechanically free and compressed LiNH4SO4 crystals. The considerable changes observed in the main reflection bands are explained by the effect of uniaxial pressures on the NH4 and SO4 tetrahedra. DOI: 10.1134/S0030400X18020169
INTRODUCTION Lithium ammonium sulfate (LAS) LiNH4SO4 crystals are classical ferroelectrics, which can exist in two modifications [1, 2]. The β modification of the LAS crystal is characterized by a pseudohexagonal tridymite-like structure consisting of vertex-sharing SO4 and LiO4 tetrahedra, which form six-membered rings perpendicular to the Z axis. The vertices of half of the tetrahedra are oriented downward, and the vertices of the other half are directed upward, where they are bound to the next tetrahedral sphere. The ammonium group (NH4) sits in the formed voids. The unit cell parameters at room temperature are a = 5.280, b = 9.140, and c = 8.786 Å [3]. In contrast to the LAS crystals of the β-modifications, the SO4 and LiO4 tetrahedra in the LAS crystals of the α-modification in the Z direction can be not only vertex-sharing but also edge-sharing. The neighboring spheres interact with nitrogen atoms of ammonium groups via hydrogen bonds, thus forming a layered structure with orthorhombic space group Pca21 and lattice parameters (T = 298 K) a = 10.196 Å, b = 4.991 Å, c = 17.100 Å, V = 870.2 Å3, and Z = 8 [4]. αmodification crystals are formed in the case of growth at room and lower temperatures, while β-modification crystals are grown at temperatures exceeding 30°С [5]. Calculation of the energy-band structure of LAS crystals using the plane-wave pseudopotential method allowed us to determine the band gap width to be Eg =
5.3 eV [6]. It was found that the valence levels are formed by a set of narrow bands separated by forbidden gaps. All levels have an insignificant dispersion, which can be explained by a relatively weak interaction between the structural elements of the crystal (NH4 and SO4 complexes). The conduction-band bottom is also characterized by a weak dispersion in the k-space and lies in point Г of the Brillouin zone. The authors suggested that the fundamental absorption edge is related to direct transitions between the valence-band top and the conduction-band bottom in point Г of the Brillouin zone. The LAS crystals have an isotropic point, because of which birefringence in the direction of the bisectrix of the angle between the optical axes at wavelength λ = 633 nm and temperature Т = 300 K is equal to zero, ∆ny = 0 [7]. The study of LAS crystals in the far-IR region at room temperature [8–11] allowed the translational and librational modes of SO24 − and NH24 − groups and Li+ ions to be determined. It has been found that the dynamics of the β-LAS crystals is characterized by 96 IR-active modes. The tetrahedral sulfate and ammonium groups can be considered as molecular units, which are relatively weakly bound to the lattice. Of the total amount of central modes, 54 are internal modes belonging to sulfate and ammonium ions, while the others are external rotational and translational optical modes. Temperature changes in the IR
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spectra of α-LAS crystals showed that heating of crystals leads to a gradual disappearance of external modes, which characterize vibrational motions of SO24 − and NH24 − groups. Despite the aforesaid, the influence of external fields on the IR spectra of LAS crystals has not been studied. Previous investigations of the effect of uniaxial pressure on the spectral and temperature dependences of refractive indices of some crystals isomorphous to LAS revealed a pronounced baric sensitivity of the electronic subsystem of these crystals, which manifested itself in a considerable energy shift of the effective bands of UV and IR oscillators [12–14]. Therefore, it is of interest to study the influence of uniaxial pressures on the IR spectra of LAS crystals to understand their selective effect on the dynamics and spatial orientation of individual structural elements of these crystals.
I, arb. units
THE EFFECT OF UNIAXIAL PRESSURES
1600 1400 1200 1000
X
1400 1200 1000 800 1000
Y
217
Z
1600 1200 800 1000
1500 ω, cm−1
2000
Fig. 1. IR reflection spectra of the LiNH4SO4 crystal at room temperature for Х, Y, and Z directions.
EXPERIMENTAL The effect of uniaxial pressures on the IR spectra of LAS crystals was studied using an UR-20 prism spectrophotometer equipped with special devices to apply uniaxial pressure. The UR-20 spectrophotometer allows one to perform measurements within the range of 400–5000 сm–1 (25–2 μm). The LAS crystals were grown from an aqueous solution by cooling. Initial materials were Li2SO4 and (NH4)2SO4. The required salt solution was obtained by mixing the initial components in the stoichiometric proportion: Li2SO4 + (NH4)2SO4 → 2LiNH4SO4. The samples were oriented by conoscopic patterns using a polarized-light microscope. RESULTS AND DISCUSSION Figure 1 shows the IR spectra of LiNH4SO4 crystals of α-modification measured at room temperature for three directions of light reflection within the range of 600–2000 сm–1. This range exhibits two clear bands peaking at 1210–1214 and 1455–1476 сm–1 with pronounced dispersion (Table 1). According to the group theory, the free radical of the tetrahedral structure has symmetry Тd and nine internal modes: single longitudinal (v1), double transverse (v2 ), triple longitudinal (v3 ), and triple transverse (v4 ), among which only ν3 and ν4 are active in the IR region [15]. The v1 and v2 modes in the crystal split into nondegenerate modes and become also active in the IR absorption spectra. The modes with v3 = 1210– 1214 сm–1 and v4 = 1455–1476 сm–1 correspond to OPTICS AND SPECTROSCOPY
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vibrations of the SO4 and NH4 tetrahedra, respectively. The IR reflection spectra of LiNH4SO4 crystals were studied at room temperature and different uniaxial pressures (Figs. 2–4). It is found that uniaxial pressure along the main crystallophysical directions leads to considerable changes in the IR reflection spectra of LiNH4SO4 crystals. In particular, the reflection spectra of LiNH4SO4 crystals in the X direction at room temperature exhibit a shift of the v3 band by 14 сm–1 to lower energies and a shift of the v4 band by 3 сm–1 to higher energies under action of uniaxial pressure along the Z axis. These bands in the reflection spectra in the Y direction shift to lower energies by 23 cm–1 (v3 ) and 1 cm–1 (v4 ). In the reflection spectra in the Z direction, the v3 band shifts by 17 сm–1 to lower energies and the v4 band shifts by 6 сm–1 to higher energies at room temperature for different uniaxial pressures along the Y axis. Table 1. Baric changes in the positions of reflection bands (сm–1) of the LiNH4SO4 crystal at room temperature Crystallophysical direction X Y Z
v3, сm–1
v4 , сm–1
σ=0
σ = σm
σ=0
σ = σm
1214 1210 1213
1200 1187 1196
1476 1455 1456
1479 1454 1462
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1800
1800 0 bar 16 bar 32 bar 48 bar 64 bar 80 bar
1400
1600
0 bar 42 bar 63 bar 84 bar
1400 I, arb. units
I, arb. units
1600
1200
1000
1200
800 1000 800
600 600
900
1200 1500 ω, cm−1
1800
400
2100
600
900
1200 1500 ω, cm−1
1800
2100
Fig. 2. IR reflection spectra in the X direction of the LiNH4SO4 crystal at room temperature for different values of uniaxial compression along the Z axis.
Fig. 3. IR reflection spectra in the Y direction of the LiNH4SO4 crystal at room temperature for different values of uniaxial compression along the X axis.
Comparison of the data obtained for the LAS crystal with the data for the isomorphous (NH4)2SO4 crystal [16] shows a shift of peaks to higher energies. In particular, the reflection spectra of LiNH4SO4 crystals in the X direction at room temperature show a shift of the v3 and v4 bands to higher energies by 50 and 15 cm–1, respectively, with respect to the corresponding positions for the (NH4)2SO4 crystal. In reflection spectra in the Y direction, the v3 band shifts by 50 сm–1 and the v4 band shifts by 9 сm–1 to higher energies. In the reflection spectra in the Z direction, these bands also shift to higher energies, by 58 cm–1 (v3 ) and 11 cm–1 (v4 ). We found a considerable difference in the shifts of the IR reflection maxima caused by uniaxial pressures in the (NH4)2SO4 and LiNH4SO4 crystals. The positions of the maxima of the v3 and v4 bands in the Х direction of the (NH4)2SO4 crystal shift by 5 and 4 сm–1, respectively, to longer wavelengths. The position of the ν3 band for the LiNH4SO4 crystal shifts by 14 сm–1 to longer wavelengths, while the position of the v4 band shifts by 3 сm–1 to shorter wavelengths. The positions of the reflections peaks v3 and v4 in the Y direction of the (NH4)2SO4 crystal shift by 4 and 3 сm–1 to shorter wavelengths, while the positions of these bands for the LiNH4SO4 crystal shift to longer wavelengths by 23 and 1 сm–1, respectively. In the Z direction of the (NH4)2SO4 crystal, the ν3 and ν4 bands shift to shorter wavelengths by 3 and 4 сm–1, while the v3 band in the LiNH4SO4 crystal shifts by 17 сm–1 to longer wavelengths and the v4 band shifts by 6 сm–1 to shorter wavelengths. In addition to changes caused by uniaxial pressures in the positions of peaks, we also observed a change in
the intensity of reflected beams. For example, the intensity of the reflection spectra in the X direction increased as the uniaxial pressure along the Z axis increased up to 16 bar and then, with increasing pressure from 32 to 80 bar, sharply decreased with respect to the free crystal. The v3 band intensity in the Y direction of the LiNH4SO4 crystal at room temperature increased with respect to the intensity in the free crystal as the uniaxial pressure increased to 42 bar and then sharply decreased in the range of uniaxial pressures from 63 to 84 bar, while the v4 band intensity continuously increased with increasing uniaxial pressure. The intensity of reflected beams for the Z direction of the LiNH4SO4 crystal at room temperature increased with respect to the intensity in the free crystal as the uniaxial pressure along the Y axis increased to 34 bar, then
2200
0 bar 17 bar 34 bar 50 bar 67 bar 84 bar
I, arb. units
2000 1800 1600 1400 1200 1000 600
900
1200 1500 ω, cm−1
1800
2100
Fig. 4. IR reflection spectra in the Z direction of the LiNH4SO4 crystal at room temperature for different values of uniaxial compression along the Y axis.
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THE EFFECT OF UNIAXIAL PRESSURES
n − 1 = 4 πN α (1) 2 n +2 3 (n is the refractive index, α is the electronic polarizability, and N is the number of particles per unit volume), one can see that an increase in the refractive index due to uniaxial compression leads to an increase in αi of the crystal. Figure 5 also demonstrates a slight baric shift of peaks in the IR reflection spectra. From the calculated dispersion curves of the real (ε1) part of the permittivity, we determined the frequencies of longitudinal oscillations vLO as the minima of function ε1 and the frequencies of transverse oscillations v TO as the maxima of function ε2 for mechanically free and uniaxially compressed crystals (Table 2). Decay constant γ was determined as the halfwidth of the corresponding peak of the ε2 curve, and the oscillator strength was determined as 2
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Y
3
Z
2 1 1000
1250 ν, cm
1500 −1
Fig. 5. Spectral dependences of refractive index ni of LiNH4SO4 crystals at room temperature for different polarizations and directions of pressures σm = 100 bar; the solid and dashed lines correspond to free and compressed samples, respectively.
As is seen from Table 2, uniaxial pressures σх and σy cause a decrease in the frequencies of longitudinal and transverse oscillations in both reflection bands, while pressures σz shift these frequencies to higher energies. In addition, uniaxial pressures along three crystallophysical directions decrease the decay constant and the oscillator strength of band III and increase the oscillator strength of band II. The results obtained are explained by the effect of uniaxial pressures on the structure of the crystal studied. The crystal structure at room temperature is disordered with respect to the orientation of tetrahedral Table 2. Frequencies (сm–1) of longitudinal (vLO ) and transverse (v TO ) oscillations, decay constant γ, and oscillator strength f of mechanically free and compressed (σm = 100 bar) LiNH4SO4 crystals Direction E || X
(2)
where n is the refractive index on the high-frequency side of the corresponding band.
X
5 4 3 2 1
E || Y
f ∼ n2(vLO – v TO ),
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4 3 2 1
ni
decreased with increasing pressure, and increased again at σ ~ 84 bar. In general, the absorption coefficient of the LiNH4SO4 crystal behaves differently for different values of uniaxial pressures. Knowing the reflection spectra, we used the Kramers–Kronig dispersion relations to determine the baric changes in the spectral dependences of refractive index n and real ε1 and imaginary ε2 parts of the LAS crystal permittivity along three crystallophysical axes. It was found that the refractive index sharply increases in the region of absorption bands, i.e., ∂n/∂λ ∼ 4.52 μm–1 (v3 band) and 2.47 μm–1 (v4 band) (Fig. 5). The change in the refractive index far from the absorption band corresponds to normal dispersion ∂n/∂λ < 0. Comparison of the normal dispersion in these regions with the dispersion in the visible region shows that they are approximately the same. For example, ∂n/∂λ is ~0.012 μm–1 in the spectral range of 1100–1200 сm–1 and ~0.01 μm–1 in the visible region (the latter value is determined by measuring the refractive index by the Obreimov interference method). As is seen from Fig. 5, the refractive index in the X and Y directions considerably increases, δn ∼ 0.55– 0.78, while the refractive index in the Z direction decreases. The character of changes in the refractive index in the IR region replicates the behavior of n in the visible region. Previously [12–14], baric increase in refractive indices δn ∼ 10–2–10–3 was found for most crystals of the A2BX4 type (LiKSO4, LiRbSO4, RbNH4SO4, and (NH4)2BeF4), which is caused, first of all, by an increase in the density of crystals. From the well-known Lorentz–Lorenz formula
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E || Z
vLO
γ
v TO
f
σ=0
σ
σ=0
σ
σ=0
σ
1214 1476 1210 1455 1213 1456
1201 1479 1187 1454 1216 1460
1184 1454 1192 1430 1184 1428
1172 1449 1170 1428 1187 1434
42 66 25 79 38 62
34 67 21 71 33 59
σ=0
σ
118 115 65 51 114 115 79 69 101 104 75 69
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T groups, which execute large-amplitude librational vibrations around the pseudohexagonal axis Z and the Y axis. The unit cell of the LiNH4SO4 crystal contains two pseudohexagonal frames with SO4 and и NH4 tetrahedra oriented along different crystallophysical axes. Application of uniaxial pressures along different axes will slow down or accelerate the rotations of T groups and thus somewhat deform the unit cell. This manifests itself in decrease or increase in the frequencies of longitudinal and transverse oscillations under pressure. The observed baric decrease in the oscillator strengths of corresponding bands indicates a decrease in the high-amplitude librational vibrations of both SO4 and NH4 tetrahedra. Since the observed baric changes both in intensity and frequency were more pronounced for band v3 , which is responsible for vibrations of the SO4 tetrahedron, we may suggest that mainly these vibrations determine the physical properties of the crystal studied, but the role played by vibrations of NH4 tetrahedra also should not be underestimated. Thus, we have studied for the first time the IR reflection spectra of mechanically free and uniaxially compressed LAS crystals in the spectral range of 800– 1700 cm–1 along three crystallophysical directions. Using the Kramers–Kronig relations, we obtained the dispersion and baric dependences of refractive index n and calculated parameters characterizing the IR dispersion, i.e., the frequencies of longitudinal (ωLO) and transverse (ωТO) oscillations, decay constant γ, and oscillator strength f of mechanically free and uniaxially compressed LiNH4SO4 crystals. Considerable baric changes are observed both in the intensity and frequency of main reflection bands, which are explained by the effect of uniaxial pressures on the
crystal structure—specifically, on the NH4 and SO4 tetrahedral cages. REFERENCES 1. P. Groth, Chemische Kristallographie (W. Engelmann, Leizpig, 1908). 2. M. Polska, Phase Transitions 12, 409 (2001). 3. A. Pietraszko, Pol. J. Chem. 66, 2057 (1992). 4. T. Nakamura, S. Kojima, and M. Takashige, Jpn. J. Appl. Phys. 18, 711 (1979). 5. P. E. Tomaszewski, Solid State Commun. 81, 333 (1992). 6. M. Ya. Rudysh, V. Yo. Stadnyk, R. S. Brezvin, and P. A. Shchepanskii, Phys. Solid State 57, 53 (2015). 7. V. Y. Stadnyk, R. S. Brezvin, and P. V. Savchuk, Opt. Spectrosc. 113, 288 (2012). 8. S. Alam and J. P. Srivastava, Spectrochim. Acta, Part A 37, 183 (1981). 9. V. I. Torgashev, Y. I. Yuzyuk, and F. Smutny, Phys. Status Solidi 135, 93 (1986). 10. I. Sosnowska, B. Hilczer, and P. Pskunowicz, Solid State Commun. 74, 1249 (1990). 11. M. Polonska, B. Hilczer, and J. Baran, J. Mol. Struct. 325, 105 (1994). 12. V. Yo. Stadnyk, V. M. Gaba, B. V. Andrievskii, and Z. O. Kohut, Phys. Solid State 53, 131 (2011). 13. V. J. Stadnyk and M. O. Romanyuk, Phys. Status Solidi A 158, 289 (1996). 14. B. Andriyevsky, M. Romanyuk, and V. Stadnyk, J. Phys. Chem. Solids 70, 1109 (2009). 15. D. Komornicka, M. Wołcyrz, and A. Pietraszko, Solid State Chem. 230, 325 (2015). 16. V. Y. Stadnyk, M. O. Romanyuk, and N. R. Tuzyak, Phys. Solid State 49, 696 (2007).
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Translated by M. Basieva
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