A. Audzijonis

Soft mode and its electronic potential in SbSI-type mixed crystals

The paper presents the results of ferroelectric dispersion at microwaves and of calculation of electronic potential dependence upon normal coordinates of B1u mode in paraelectric and ferroelectric phases in SbSI-type mixed crystals. Obtained large anharmonicity of the electronic potential at Sb (or Bi) site confirms the splitting of the soft B1a mode, the main component of which causes the ferroelectric dispersion at microwaves. Dependence of the electronic potential on composition revealed all factors which change the temperature of phase transition and the soft mode dynamics. It also explains why the pure SbSeI, BiSI and BiSel are not ferroelectrics.

The electronic potential of the V-VI-VII compounds in the region of phase transition

Abstract This paper deals with the dependence of the electronic potential on normal coordinates for SbSI, SbSBr, SbSeI, SbSeBr crystals at Sb, Bi, S, I, Se, Br sites in the paraelectric phase and for SbSBr crystal in the ferroelectric phase. In the paraelectric phase the normal mode of symmetry B 1u, is studied. The large anharmonicity of electronic potential implies that SbSI and SbSBr exhibit intermediate behaviour between a displacive and order-disorder phase transition. The electronic potential of the B1u mode of SbSeI, SbSeBr, BiSeI, BiSeBr, SbSCI, SbSeCl, BiSCI, BiSeCl at Sb, Bi sites is characterized by a relatively small anharmonicity within the temperature range 20–295 K. The non-ferroelectric nature of these crystals follows from the results. Because of the large atomic radius of Bi compared with Sb, a ferroelectric phase transition is also doubtful in BiSI and BiSBr crystals.

Origin of ferroelectricity in SbSI

Abstract There are three phases in the phase diagram of SbSI: ferroelectric (T 410 K). In the antiferroelectric phase the arrangement of the polar chains becomes antiparallel (up and down). It causes a disorder of the Sb atoms. Ferroelectricity and phase transitions in SbSI are closely related to its electronic structure and phonon interaction. The disorder results in an asymmetric double-well soft-mode potential. It leads to threefold splitting of the soft mode frequency. They all show large absorption peak and deep dielectric dispersion in millimeter and far IR region.

The electronic potential of SbSI crystal in the region of phase transition

The paper presents the SbSI crystal electronic potential dependence on normal coordinates at Sb, S and I sites in paraelectric and ferroelectric phases. The symmetry of investigated normal mode is paraelectric phase B1u. The large anharmonicity of electronic potential suppose that SbSI exhibits an intermediate behaviour between displacive and order-disorder phase transition.

Investigation of the Soft Mode of SbSBrxI1−x Crystals

The behaviour of the potential energy V(z) of the B 1u (A 1 ) symmetry soft mode vibrations of atoms in the direction of the z(c) axis of SbSBrxI 1−x crystals (x = 0, 0.2, 0.75, 1) upon the normal coordinate (relative displacements of atoms) was investigated in the region of the phase transition temperatures. For this B 1u (A 1 ) symmetry soft mode, the potential energy barrier height ΔV, the potential energy V(z), its harmonic and anharmonic terms were studied as functions of the mixture composition x and temperature T. The dependence of the soft mode frequency ωS upon the composition x and temperature has been established assuming the double-well shape of the potential energy (per atom) V(z). By employing A 1u (A 2 ) symmetry coordinates, the force constants C of interaction between molecular chains have been obtained. The type of the phase transition has been established by calculating the Rhodes–Wohlfarth factor R. To calculate this factor, the ratio /ΔV depending upon the mixture composition was employed. It has been found that for mixed crystals with x < 0.8, the phase transition is intermediate between order–disorder and displacive types, and for crystals with x > 0.8, the phase transition is of displacive type.

Electronic Potentials of Normal Vibrational Modes in SbSI Crystals

Symmetry and normal coordinates of vibrational modes are calculated in both para- and ferroelectric phases of SbSI crystals. The dependencies of the electronic potential (EP) in the paraelectric phase upon the normal coordinates of all D 16 2 h symmetry normal modes formed by displacements of the atoms along the c axis are studied for SbSI. It is found that part of these modes are weakly anharmonic with EP having a single minimum and another part are strongly anharmonic with a double-well EP. Potentials with double-well EP form the soft mode of B 1 u symmetry in the microwave range and semisoft modes in the IR range. EP of all D 16 2 h symmetry normal modes were used for the interpretation of reflectivity spectra for E Á c in the para- and ferroelectric phases of SbSI crystals.

Splitting of the XPS in Ferroelectric SbSBr Crystals

This paper presents the theoretical investigation of energy of core levels (CL) of the ferroelectric SbSBr single crystals in paraelectric and ferroelectric phases. Since the best approximation for the CL levels is a calculation by the Hartree-Fock method, the molecular model of SbSI crystal was used for calculations. It was found that CL of this semiconductor ferroelectric are sensitive to the small lattice distortion at phase transition, and on ion charges. The experimental splitting of CL obtained by XPS was compared with theoretically calculated one by two different methods. The cluster model calculations showed that the splitting of the CL in SbSBr might be caused by photoelectron emission from the atoms, which have different ion charges at the surface. Communicated by Dr. George W. Taylor

Theoretical investigation of the electronic structure of a ferroelectric SbSI cluster at a phase transition

This paper presents the theoretical investigation of energy levels of valence bands (VB) and core levels (CL) of the ferroelectric SbSl single crystals in antiferroelectric and ferroelectric phases. Since the best approximation for the deep VB levels is a calculation by the Hartree-Fock method, the molecular model of a SbSI crystal was used for calculations. This model of the crystal was also used for calculations of the total density of states. It was found that the VB and CL of this ferroelectric semiconductor are sensitive to the small lattice distortion at the phase transition, and that an average of the total density of states, when all atoms participate in oscillations of all normal modes, are more similar to the experimental X-ray photoelectron spectra (XPS). The experimental splitting of CL obtained by XPS was compared with the theoretically calculated one by two different methods. The cluster model calculations showed that the splitting of the CL in SbSI might be caused by photoelectron emission from the atoms, which have different valence state, at the surface.

Peculiarities and properties of SbSI electroceramics

SbSI ferroelectric electroceramics has been developed with the increased Curie temperature (T c =58°C). Below T c , the electroceramics possess high volume piezoelectric modulus and other parameters important for applications. Microwave and far IR studies reveled that the main dielectric dispersion lies in the range 1-100 GHz. Ab initio calculations of the soft B 1u mode potential have shown that in paraelectric (PE) phase on approaching T c it becomes of a double well form. The high harmonicity splits the soft mode. The lowest frequency component lies at microwaves and gives the main contribution (Δe m = 25,0000) to static permittivity which follows the Curie-Weiss law. The contribution of IR component (Δe 1R = 1500) weakly depends on temperature.

Variation of the SbSI crystal energy gap at phase transition

Abstract Variation of the forbidden gap of SbSI crystals in the phase transition region is analyzed on the basis of calculations using the empirical pseudopotential method for the paraelectric (PEP) and ferroelectric phase (FEP). Other theoretical SbSI studies are critically reviewed. The band gap at several special points of the Brillouin zone and some characteristic parameters of the band structure are considered. At the ferroelectric phase transition, the variation of the direct and indirect gaps is mainly determined by variation of coupling between 3p-orbitals of S and 5p-orbitals of Sb. During the phase transition, the most significant changes are observed with the valence band top at points Q, C, R, H, E and with the conduction band bottom at points H, T and E of the Brillouin zone.