Critical behaviour of Sn2P2S6 and Sn2P2(Se0.28S0.72)6 crystals under high hydrostatic pressures

Basing on the temperature dependences of optical birefringence for Sn₂P₂S₆ and Sn₂P₂(Se_0.28S_0.72)₆ crystals subjected to hydrostatic pressures, we prove unambiguously that Sn₂P₂S₆ reveals a tricritical point on its (p, T)-phase diagram with the coordinates (p, T) = (4.3 kbar, 259 K), so that the second-order phase transition transforms into the first-order one whenever the pressure increases above 4.3 kbar. We also find that increasing hydrostatic pressure applied to Sn₂P₂(Se_0.28S_0.72)₆ leads to the change in the phase transition character from tricritical to first order. Further increase in the pressure up to ~2.5 kbar imposes splitting of the first-order paraelectric-to-ferroelectric phase transition into two phase transitions, a second-order paraelectric-to-incommensurate one and a first-order incommensurate-to-ferroelectric transition.     

Dielectric properties of Sn2P2S6 crystals as a function of their growth conditions

The behavior of the permittivity near a phase transition in Sn₂P₂S₆ crystals of different technological quality is studied. It is established that, in high-resistance crystals, where an internal electric field is formed by the screening of spontaneous polarization in the polar phase, long-time relaxation of ɛ is observed in a temperature range ∼2 K above T _max. This relaxation and change in the form of the maximum of ɛ′(T) at a phase transition are attributed to an internal electric field induced by the volume space charge formed in regions near the surface. It is established that the existing differences in the properties of Sn₂P₂S₆ crystals are due to deviations from stoichiometry, arising during growth and synthesis of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1456–1461 (August 1999)     

Thermal expansion of Sn2P2S6 crystals

We present the results for thermal expansion coefficients of Sn₂P₂S₆ crystals determined both in the crystallographic system and the system based on eigenvectors of thermal expansion tensor. Peculiarities of temperature evolution of the indicative surface of thermal expansion tensor for Sn₂P₂S₆ are discussed, including the region of their ferroelectric phase transition.     

New phase-transformation line and intermediate phase in Sn2P2S6

A study is made of the effect of temperature and hydrostatic pressure on the permittivity, forbidden-band width, electrical conductivity, and photoconductivity of crystals of Sn₂P₂S₆. The empirical results obtained indicate that a new phase-transformation line exists on the p-T diagram of Sn₂P₂S₆ p > 0.17 GPa. This phase transformation is evidently a second-order transition, separating a paraelectric, proportionate phase from an intermediate, possibly nonproportionate phase. The results also indicate similarity of the p-T diagram of Sn₂P₂S₆ to the x-T diagrams of ferroelectric solid solutions of Sn₂P₂(Se_xS_1–x)₆.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–60, September, 1985.     

Microwave study of the soft ferroelectric mode in Sn2P2S6 crystals

This paper presents the results of the investigation of dielectric dispersion in semiconductive ferroelectric Sn₂P₂S₆ crystals over the frequency range 1 kHz to 78.5 GHz. The main dielectric dispersion in Sn₂P₂S₆ is caused by the soft ferroelectric B_u mode and in the vicinity of the Curie point it occurs in the millimeter region. The frequency of the soft mode in the paraelectric phase varies according to v_s = 35 (T-T_c )^½ GHz on approaching the Curie point. The soft mode is strongly overdamped. Close to T_c the relative damping is y/v_s = 14. The dielectric contribution of the soft mode is equal to the static dielectric permittivity and it explains its whole temperature-dependence.     

Thermal expansion of the Sn2P2(Se0.28S0.72)6 solid solutions

In the present work, we have experimentally studied and analysed the dilatometric properties of Sn₂P₂(Se_0.28S_0.72)₆ crystals during ferroelectric phase transition. A complete matrix of thermal expansion tensors as well as the characteristic surface of the thermal expansion tensor has been obtained. The critical exponent for the volume thermal expansion coefficient in Sn₂P₂(Se_0.28S_0.72)₆ crystals has been determined to be equal to 0.50 ± 0.06, which is peculiar to tricritical behaviour. Non-agreement in the values of the critical exponents evaluated from the temperature dependencies of relative elongation (0.17 ± 0.01) and volume thermal expansion coefficient (0.50 ± 0.06) is shown to be due to the possible temperature rotation of the spontaneous polarisation vector.     

On the tricritical point on the (p,T)-phase diagram of Sn2P2S6 crystals

Using studies of the temperature dependence of the acoustic wave velocity at high hydrostatic pressures, a tricritical point where second-order phase transitions change to first-order ones was experimentally revealed on the pressure–temperature phase diagram of Sn₂P₂S₆ crystals. The behavior of the acoustic wave velocity is explained in the framework of mean-field theory.     

Acoustic wave velocities and elastic properties of Sn2P2(Se0.28S0.72)6 solid solutions

An experimental study and analysis is presented of the acoustic properties of Sn₂P₂(Se_0.28S_0.72)₆ ferroelectric crystals. Complete matrices of elastic stiffness and compliance as well as characteristic acoustic slowness surfaces have been obtained. The directions of propagation and polarisation of the slowest acoustic waves were determined. It was found that the elastic properties and the acoustic wave velocities for Sn₂P₂(Se_0.28S_0.72)₆ and Sn₂P₂S₆ crystals are almost the same at room temperature.     

Investigation of the dielectric,optical and photorefractive properties of Sb-doped Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals

In this work we report results on electro-physical, optical and photorefractive investigations for Sb-doped Sn₂P₂S₆ crystals. The crystals are obtained by two methods: the vapour-transport technique and the Bridgman technique using stoichiometric Sn₂P₂S₆ composition with different amounts of antimony in the initial compound. The good optical quality of the crystals obtained with the Bridgman technique is underlined. The dependences of the photorefractive two-beam coupling coefficient and the grating build-up time are investigated at the wavelength of 633 nm. It is found that the sample doped with 1.5% of Sb is characterized by an optimal combination of the main photorefractive parameters exhibiting a fairly high two-beam coupling coefficient (up to 20 cm⁻¹) and a short response time (1.3 ms) that is the shortest among all the previously studied Sn₂P₂S₆ crystals in the red spectral region.     

Band structure and model of the paraelectric structure of the Sn2P2S6 crystal

Since a variety of choices exist in the literature for the symbol of the space group of crystals of the type Sn₂P₂S₆, hindering the use of a group-theoretic analysis to determine the properties of the band spectrum and phonon spectrum, identified this symbol is identified with the known coordinates of the atoms of the given crystals. It is shown that the different arrangements P2₁/c and P2₁/n lead to permutations of the points in the Brillouin zone and correspondingly to a change in the irreducible representations. Calculating the spectra of Sn₂P₂S₆ and Sn₂P₂Se₆ by the method of pseudopotentials fitted to the width of the bandgap confirms the double degeneracy at the X, Y, Z points of the Brillouin zone, which was not expected for the X point in the arrangement P2₁/c. We have detected the previously predicted minimal band complexes in the band spectrum, which are the same as for In₄Se₃ of the group D _2h ¹² . Fiz. Tverd. Tela (St. Petersburg) 39, 1219–1222 (July 1997)     

On the special points on the (P,T, x)-phase diagram for Sn2P2(Se x S1− x )6 crystals: acoustic studies of Sn2P2(Se0.28S0.72)6

On the basis of temperature dependences of the acoustic wave velocity and the acoustic attenuation in Sn₂P₂(Se_0.28S_0.72)₆ crystals under normal conditions and hydrostatic pressures, we show that increasing pressure causes these crystals to move away from the tricritical point and enter into the region of first-order phase transitions (PTs) in (P,?T,?x)-space. Still higher hydrostatic pressures lead to an increase in the attenuation of the acoustic wave with the velocity v ₂₂ and broadening of its anomaly in the PT region, thus hinting at splitting of the PT, with the appearance of an intermediate incommensurate phase approximately at P?=?3.3?kbar. We offer a (P,?T,?x)-phase diagram for the solid solutions Sn₂P₂(Se _x S_{1? x} )₆, which includes two special lines of PTs, tricritical and triple ones, which can intersect at the Lifshitz point at negative hydrostatic pressures. The variations of the surface of acoustic wave velocities occurring with changing temperature are obtained for Sn₂P₂(Se_0.28S_0.72)₆ crystals under the atmospheric pressure.     

Acoustic attenuation in ferroelectric Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals

The temperature and frequency dependencies of sound attenuation for the proper uniaxial ferroelectric Sn₂P₂S₆, which has a strong nonlinear interaction of the polar soft optic and fully symmetrical optic modes that is related to the triple well potential, were studied by Brillouin spectroscopy. It was found that the sound velocity anomaly is described in the Landau-Khalatnikov approximation with one relaxation time. For explanation of the observed temperature and frequency dependencies of the sound attenuation in the ferroelectrric phase, the accounting of several relaxation times is needed and, for quantitative calculations, the mode Gruneisen coefficients are more appropriate as interacting parameters than are the electrostrictive coefficients. Relaxational sound attenuation by domain walls also appears in the ferroelectric phase of Sn₂P₂S₆ crystals.     

Splitting of the phase transition in ferroelectric solid solutions Sn2P2(SexS1−x)6 at high pressures

The influence of the temperature and hydrostatic pressure on the forbidden band width and dielectric permittivity of the ferroelectric solid solutions Sn₂P₂(Se_xS_1–x)₆ (x=0.04, 0.20, 0.30) is investigated. A change in the species and splitting of ferroelectric phase transition lines are detected for p = 0.140 and 0.026 GPa, respectively, for the solid solutions Sn₂P₂(Se_0.04S_0.96)₆ and Sn₂P₂(Se_0.20S_{0.80 6}, which is due to the existence of a Lifshits critical point separating the transitions into codimensional and noncodimensional phases on the p, T diagram. Shift coefficients with the pressure of the phase transition temperature are found for the solid solutions investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 28–32, February, 1988.     

Coherent semilinear oscillator with Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript>:Sb crystals

We present experimental results for the semilinear oscillator geometry based on Sn₂P₂S₆:Sb photorefractive crystals. The samples with strong two-wave mixing gain demonstrate degenerate oscillation regime. A mirrorless oscillation is also observed.     

Determination of the absorption constant in the interband region by photocurrent measurements

We determined high absorption constants of crystals from photocurrent measurements within the interband absorption region (10–10⁴ cm^-1). The method has been demonstrated in the interband absorption regime near 530 nm in Sn₂P₂S₆, a novel infrared sensitive photorefractive material, and in the interband absorption regime near 257 nm of near stoichiometric LiTaO₃. Besides the verification of older measurements with our new technique, precise absorption data for Sn₂P₂S₆ in the wavelength range 488–514 nm are presented. PACS 42.70.Nq; 72.41.+w; 78.20.Ci     

About the existence of a Lifshitz point on the phase diagram of Sn2P2(Se x S1– x )6 solid solutions: acoustic and optical studies

On the basis of combined studies of the acoustic and optical properties of Sn₂P₂(Se _x S_{1– x} )₆ solid solutions with x?=?0 and 0.28 it is shown that two special points exist on the x,T-phase diagram of these ferroelectric crystals, a tricritical point and a triple one. With increasing Se concentration, the phase transition changes its character at x?≈?0.28 from second-order to first-order. The phase transition becomes split at x?≈?0.4, with the appearance of an intermediate incommensurate phase.     

Temperature behavior of the photovoltaic and pyroelectric responses of Sn2P2S6 semiconductor ferroelectric films

The electric response of Sn₂P₂S₆ semiconductor ferroelectric films to focused laser radiation (λ = 6328 Å) with a modulation frequency of 24 Hz is studied experimentally. It is shown that the signal involves an initial spike of current (an unsteady component) followed by the relaxation decrease to a certain value (a quasisteady component). The most significant changes in the shape and amplitude of the film response is observed near the Sn₂P₂S₆ monocrystal phase transition point of T _C = 66°C. The behavior of the unsteady component of the response is related to the behavior of the spontaneous polarization. This component decreases with increasing temperature. The quasi-steady component reaches its maximum at T = C _C. It is revealed that the behavior of relaxation processes corresponding to the decreasing response undergoes a change near the phase transition temperature.     

Transient short-circuit photocurrent in ferroelectric semiconductor Sn2P2S6 films

Transient short-circuit photocurrents in films of the ferroelectric semiconductor Sn₂P₂S₆ are studied in a temperature range that includes the phase transition point. The influence of an external electric field and white-light illumination on the photoelectric response of samples is discussed.     

Dynamically reconfigurable characteristics of a double phase conjugate mirror using Sn2P2S6 crystals and their application to optical inter-satellite communication

A double phase conjugate mirror (DPCM), created by two mutually incoherent beams entering photorefractive nonlinear materials, can generate a phase conjugate beam whose reflectivity may be greater than 100%. Even though the conditions of the incident beams are changed, the DPCM can be dynamically reconfigured by using a Sn₂P₂S₆ crystal with a high response speed. These features of the DPCM are advantageous, particularly in an optical inter-satellite communication system. In particular, use of the phase conjugate beam from the DPCM offers wavefront compensation and amplification in satellite communication. In addition, the dynamically reconfigurable DPCM using a Sn₂P₂S₆ crystal relaxes the acquisition accuracy of the signal beam in the system. In this study, the temporal and spatial operating characteristics of the DPCM using a Sn2P2S6 crystal were first clarified. Next, an inter-satellite system based on the DPCM was proposed, and it was demonstrated that our system significantly improves the tolerance of the acquisition accuracy and tracking time.     

Dynamic shift of the phase-transition temperature in (Sn1−x In(2/3)x)2P2S6 crystals with incommensurate phase

The dielectric properties of ferroelectric (Sn_1?x In_(2/3)x )₂P₂S₆ crystals were studied in the region of incommensurate phase transitions occurring upon fast cooling and heating (0.2–11 K/min). The dynamic phase-transition shift observed in these materials was examined.