R. Žaltauskas

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.

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.

Electronic band structure of ferroelectric semiconductor SbSi studied by empirical pseudopotential

Abstract The choice of the empirical pseudopotential method for studying the electronic band structure of SbSI-type crystals is discussed. The method is applied to study the SbSI crystal in the paraelectric and ferroelectric phases. Differently from previous studies, a covalent crystal structure is assumed. The total density of states is calculated using the tetrahedron technique modified for treating orthorhombic crystals. The calculated total density of states is compared with the experimental X-ray spectroscopy data indicating good agreement between the theory and experiment. The composition of the bands is discussed. According to the calculations, in PEP the SbSI crystal shows indirect transition between points U and Z of the Brillouin zone, and in FEP it is between points R and Z. The minimum direct gap is for both phases at point U of the Brillouin zone.

Origin of the Optical Anomalies Near the Ferroelectric Phase Transition in SbSI and SbSBr Crystals

Experimental investigation of SbSI exponential absorption tail of slope σ/kT(T) and isoabsorption energy E K (T) at K = const reveal that in ferroelectric phase transition region at T c the slope σ/kT(T) has anomalous behavior. Explanation of this phenomena presented using electronic potential V(z) dependence upon high frequency mode B1u symmetry normal coordinates in (z) direction taking into account thermal fluctuations of the atoms in x − y plane. The splitting of B1u normal modes in double-well V(z) explains anomalous behavior σ/kT(T) at the ferroelectric phase transition region in SbSI and SbSBr crystals.

Theoretical investigation of the electronic structure of ferroelectric SbSBr molecular cluster

This paper presents the theoretical calculation of energy levels of the valence bands and bond orders of the SbSBr single crystals using the molecular cluster model consisting twenty SbSBr molecules. The theoretical calculation revealed that the ferroelectric phase transition changes the bond orders and shift valence bands. Results of theoretical calculations of averaged total density of states of SbSBr molecular cluster are compared with the experimentally results of X-ray photoelectron spectroscopy (XPS) of SbSI crystals, because that SbSI and SbSBr crystals have isomorphic electronic structure.

Birefringence and refractive indices of ferroelectric SbSI

Electronic structure and refractive indices of SbSI crystal in paraelectric and ferroelectric phases were investigated by full-potential linearized augmented plane wave method with density functional theory. The temperature dependence of refractive indices along a-, b-, and c -axes and birefringence Δn = nc  − na as a function of photon energy were calculated near the phase transitions. The theoretical results were compared with experimental measurements of birefringence. Comparison between calculated increment of the birefringence δ(Δn 0 = nc  − na ) and experimental spontaneous polarization indicates the existence of the second-order phase transition at Tc 2 ≈ 240 K and confirms its relation to the P s.

The nature of anharmonicity and phase transition in SbSBr crystal

The ferroelectric crystal structure of SbSBr is composed of [Sb(S, Br)]∞ chains parallel to the [001] axis. In paraelectric phase, the crystal structure is disordered. The theoretical investigation of dependence of potential energy VP (z) of Sb atoms on amplitudes of B1u vibration symmetry coordinates along c (z)-axis have showed that each atom is shifted from the xy mirror plane by up or down along [001]. The theoretical investigation of the average potential energy of all Sb atoms in unit cell revealed that in paraelectric phase in region of phase transition has double-well shape. This strong anharmonicity of is created by interaction between phonons.