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 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.     

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.     

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.     

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.     

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.     

Baric dependence of the fundamental absorption edge in the region of phase transitions of Sn2P2S6-type intrinsic ferroelectrics

The energy position of the fundamental absorption edge in the neighborhood of phase transitions in Sn₂P₂S₆ and (Pb_0.1Sn_0.9)₂P₂S₆ ferroelectric crystals is studied as a function of the temperature and baric dependence on the basis of direct measurements of the isoabsorption relations. Thep, T phase diagram of Sn₂P₂S₆ crystals is constructed. the temperature-dependent variation of the band gap in those crystals is due mainly to electron-phonon interaction. Uzhgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 82–85, August, 1997.     

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)     

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 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.     

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.     

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.     

Multicritical behavior in ferroelectrics

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (Pb_ySn_1y)₂P₂(Se_xS_1-x)₆. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.     

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.     

Anomalous X-ray scattering studies on superionic glassy (As2Se3)-(AgX) systems (X = halides)

Anomalous X-ray scattering experiments for glassy room-temperature superionic conductors (As₂Se₃)_0.4 (AgI)_0.6 and (As₂Se₃)_0.4(AgBr)_0.6 were performed close to the As, Se, Ag, and Br K edges using a third-generation synchrotron radiation facility, ESRF. The differential structure factors, Δ_iS(Q), were obtained from detailed analyses, indicating that Δ_AsS(Q) and Δ_SeS(Q) of both the glassy superionic semiconductors are similar to those of glassy As₂ Se₃ except the prepeak in Δ_SeS(Q). The Δ_AgS(Q) spectrum of (As₂Se₃)_0.4 (AgI)_0.6 looks molten salt-like. However, the Δ_Ag S(Q) of (As₂Se₃)_0.4(AgBr)_0.6 glass have quite different features from that of (As₂Se₃)_0.4 (AgI)_0.6 glass in the low Q range, and the Δ_BrS(Q) has even a pre-shoulder around 13 nm^? 1 unlike molten salts. In the differential pair distribution functions Δ_ig(r) obtained from the Fourier transforms of Δ_iS(Q), the first peaks of Δ_Asg(r) and Δ_Seg(r) show no correlation with those of Δ_Agg(r) and Δ_Brg(r), and vice versa. From these results, it can be concluded that a pseudo-binary mixture of the As₂Se₃ network matrix and AgX-related ionic conduction pathways is a good structural model for these superionic glasses. Differences between the AgBr- and AgI mixtures were found in the second-neighbor structures around the Ag atoms, which may reflect those in the crystal structures of the AgX salts.     

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.     

Electronic and spatial structure of nanoclusters of Sn2P2S6 ferroelectric crystals

The results obtained from ab initio calculations of the optimized configuration and electronic structure of the cluster models of Sn₂P₂S₆ ferroelectric crystals are presented. The calculations have been performed using the spin-restricted Hartree-Fock method and the density functional theory in the DZVP basis set. It has been shown that the clusters are stable and retain the topology of the simulated crystal. The influence of the cluster sizes on the properties under investigation has been analyzed.     

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.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

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.