L. Žigas

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.

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.

Jahn-Teller effects in the SbSBr crystals atomic chain

The quasi-one-dimensional SbSBr atomic chain consisting of up to 60 atoms is considered theoretically. One-electron energies of atoms have been calculated using the unrestricted Hartree–Fock method within the Hw basis set employing the pseudopotential. The symmetry of normal vibrational modes of the SbSBr chain in the paraelectric and ferroelectric phases has been determined. It was shown that the A u and B g symmetry of the top electronic levels of the highest valence band are degenerated in the paraelectric phase. The low frequency and high frequency Au symmetry normal modes interacting with the degenerate Au symmetry electronic states in the top of valence band induce the Jahn-Teller effect. The same modes interacting with Au symmetry electronic states in the valence band and with B g symmetry states in the bottom of conduction band induce the pseudo Jahn-Teller effect. The total energy upon normal co-ordinates of modes and Au due to both Jan-Teller effects demonstrates anomalous variation of its vibrational frequency in the phase transition region.

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.

Investigation of Vibrational Spectra of SbOxS1–xI Crystals in the Phase Transition Region

SbOxS1 - xI (x=0–0.5) crystals have been grown from the vapour phase. Reflection spectra of the SbOxS1 - xI (x=0.2) crystals were studied by a modernized Fourier spectrometer. Using an improved Karmers–Kronig technique with two confining spectral limits, the spectra of optical parameters and optical functions were calculated. The vibrational frequenciesωLandωThave been evaluated. The vibrational frequencies of SbSI and SbOxS1 - xI (x=0.5) chains in different phases have been calculated in the harmonic approximation. The theoretical results are compared with experimental data. Taking into account the anharmonicity of the electronic structure and lattice, caused mainly by the phonon–phonon interaction, the phase transition temperature TCas a function of the mixture compositionxhas been evaluated. The dependence of the total potential energy function of the soft B1umode upon temperature determines variation of its frequencyωs2in the phase transition region.

Origin of Ferroelectric Phase Transitions of BixSb1-xSI Mixed Crystals

The nature of normal modes’ anharmonism of SbSI—type crystals is investigated in this work. In order to explain the nature of anharmonism we apply the normal vibration modes average potential energys dependence on amplitudes of normal coordinates along c (z)—axis. It is proved that the variation of potential barrier between two wells of double-well potential energy Vp(z) is caused by temperature T, quasihidrostatic pressure p, and mixture x. The temperature dependence of ferroelectric phase transition on quasihidrostatic pressure p and mixture x is determined for SbSI and BixSb1-xSI crystals. Applying the equality is theoretically proved that there is no ferroelectric phase transition in BixSb1-xSI crystals where x > 0.7. The ferroelectric phase transition in SbSI—type crystals and BixSb1-xSI crystals is caused by the phonon interactions dependence on temperature, pressure and mixture.