Experimental and theoretical investigation of vibration spectra of SbSBrxI1-x mixed crystals in harmonic and anharmonic approximation

Didelį susidomėjimą A5B6C7- tipo feroelektrikai kelia todėl, kad jie turi puslaidininkinių savybių[1]. Labiausiai iš šios klasės junginių išsiskiria SbSI. Šis kristalas yra charakterizuojamas eile unikalių savybių, tokiu kaip: didžiausias pjezomodulis iš visų šios klasės junginių, daug jautresnis išoriniam spaudimui ir t.t. Vibracinių modų anharmonizmo tyrimas yra būtinas, tam, kad galėtume nustatyti minkštosios modos ir fazinio virsmo prigimtį. SbSI-tipo kristalų minkštosios modos anharmonizmas buvo išanalizuotas skaičiuojant šių modų potencinės energijos V(z) priklausomybę nuo normaliųjų koordinačių, c(z)-ašies kryptimi, atsižvelgiant į sąveiką tarp fononų [2, 3] arba tarp fononų ir elektronų [4, 5]. Tačiau, vibracinių modų V(z), SbSI-tipo kristaluose, buvo ištirta naudojant normaliąsias koordinates, kur buvo įtraukta sąveika tarp grandinėlės atomų. Darbo tikslas- apskaičiuoti V(z) priklausomybe nuo normaliųjų koordinačių, priimant dėmesin sąveiką tarp skirtingų atominių grandinėlių pratęstų išilgai c(z)- ašies. Darbas skirtas SbSI kristalo normaliųjų koordinačių nustatymui, atsižvelgiant į sąveika tarp grandinėlių. Normaliųjų koordinačių nustatymui naudojamas dinaminės matricos diagonalizavimas. Dinaminės matricos sudarymui yra būtina žinoti standumus, kurie buvo nustatyti pseudopotencialo metodu. Po dinaminės matricos diagonalizavimo, gauname normaliąsias tikrinius vektorius – normaliąsias koordinates ir tikrines vertes- normalinius dažnius. Vibracinės modos x-y plokštumoje nebuvo nagrinėjamos, nes V(x) ir V(y) yra vienaslėnės ir nuo temperatūros bei feroelektrinio fazinio virsmo nepriklauso. Taigi tiktai V(z) nagrinėjimas yra naudingas SbSI- tipo kristalų teoriniam ir praktiniam minkštosios modos atsiradimo aiškinimui. Feroelektrinio fazinio virsmo temperatūra mišriame SbSBrxI1-x kristale, kaip parodyta darbe, stipriai priklauso nuo mišinio sudėties x. x padidėjimas sumažina fazinio virsmo temperatūrą Tc ir atvirkščiai. SbSBrxI1-x kristale yra minkštosios žemo dažnio modos- R ir IR Brijueno zonos taške k=0, Brijueno zonos taške k=0.5 minkštosios yra A ir žemo dažnio R moda.The great interest in the A5B6C7 – type ferroelectrics is caused by the fact that they possess semi-conductor properties. Also they are characterized by a number of unique properties, e.g. could be SbSI- it has the largest piezomodulus among the compounds of its class it is by an order more sensitive to the external pressure etc. Research of the anharmonicity of the vibration modes in the ferroelectric crystals is necessary for the determination of the nature of the soft mode and the phase transition. The anharmonicity of the soft mode of SbSI- type crystals has been analyzed by calculating the dependence of the potential energy of these modes on the normal coordinates V(z) in the direction of the c(z)- axis when the interaction of phonons or electron-phonons was taken into account. However, V(z) of the vibration modes of SbSI- type crystals was investigated using normal coordinates, which included interaction between different atoms in the same atomic chains. The aim of the work is to calculate V(z) dependence on normal coordinates, including the interac-tion between different atomic chains extended in the direction of the c(z)- axis. The work is attri-buted to the determination of the normal coordinates of the SbSI- crystal with the interaction between different chains. Normal coordinates are usually determined by diagonalization of the dynamic matrix. The force constants between all atoms in a chain as well as between atoms in different chains are necessary to make a dynamic matrix. Force constants were determined using pseudo-potential method. After the diagonalization of finamic matrix one gets eigenvalues-frequencies an eigenvectors- normal coordinates. A vibration modes in the x-y crystallographic plane has not been discussed because V(x) and V(y) of these modes are single-well and their sensitivity to the temperature change and ferroelectric phase transition is negligible. Thus just the research of V(z) is useful for the theoretical and pra-ctical explanation of the nature of soft and semisoft modes of SbSI- type crystals as well as their dependence on an interaction between different chains. The ferroelectric phase transition temperature in SbSBrxI1-x mixed crystals, as shown in work, strongly depends on the composition x. The increase in x gives the decrease in temperature. There are two R and IR low frequency modes (soft) which are sensitive to the temperature change when k=0 and three A, R and IR low frequency modes (soft) when k=0.5.Švietimo akademijaVytauto Didžiojo universiteta

Investigation of the vibration spectra of a SbSBrxI1-x crystal in harmonic and quasiharmonic approximation

The vibration of spectra SbSBrxI1-x (x = 0 ÷ 0.75) crystal have been determined in quasiharmonic approximation by diagonalization of dynamical matrix. Applying the model atom A with its own parameters (mass and force constants) we were able to get exact normal modes' vibration frequencies. The obtained normal modes' frequencies were superposed with experimental data. It is proved that in Brillouin zone's point k =0 the lower frequency IR (infrared) mode of B1a symmetry and lower frequency R (Raman) mode of B 1g symmetry are soft -alike modes whereas in Brilloun zone's point k = 0.5 an acoustic and Raman mode become active, but lower frequency IR mode becomes inactive. The interaction between phonones creates the anharmonicity of soft-alike IR, R and A vibration modesVytauto Didžiojo universitetasŠvietimo akademij

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 phononsVytauto Didžiojo universitetasŠvietimo akademij

The experimental and theoretical investigation of vibration spectra in ferroelectric semiconductor SbSBrxI1−x crystals

The vapor grown SbSBrxI1−x (x=0.1; 0.5; 0.9) crystals with clear mirror surfaces have been used for infrared reflection measurements with Fourier spectrometer. The vibration frequencies along c(z)-axis have been derived from Kramers–Kroning and optical parameters fitting analysis of the experimental reflectivity spectra at T=300 K. The theoretical vibration spectra of SbSBrxS1−x (x=0.1; 0.5; 0.9) crystals in paraelectric phase (T=300 K) along c(z)-axis have been determined in quasiharmonic approximation by diagonalization of dynamical matrix. The theoretical vibration spectra of these crystals in a–b(x−y) plane have been determined in harmonic approximation. In this work we discuss the nature of anharmonism in SbSBrxI1−x crystals along the c(z)-axisVytauto Didžiojo universitetasŠvietimo akademij

The nature of the ferroelectric phase transition in the modified SbSI ceramics

The modified SbSI (ceramic) has been grown by Bridgman method. The dielectric permitivity of modified SbSI along c(z)-axis has been measured using LCR meter as a function of temperature at fixed frequency 1 KHz. The nature of ferroelectric phase transition in the modified SbSI has been discussed using ab initio calculations. Theoretical investigations reveal how ferroelectricity and phase transition in the modified SbSI are closely related to deformation of the unit cell and the phonon interaction. Dielectric measurements reveal that substitution of the individual (I−) with (Cl−) ions creates the deformation of the unit cell and increase the temperature of the ferroelectric phase transition TC. Deformations of the unit cell change the interaction between phonons and the anharmonicity of soft B1u normal modeVytauto Didžiojo universitetasŠvietimo akademij

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 mode's average potential energy' s p (z) dependence on amplitudes of normal coordinates along c(z) -axis. It is proved that the variation of potential barrier Vc between two wells of double-well potential energyu 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 V c = kbTc is theoretically proved that there is no ferroelctric phase transition in BixSb1-xSI crystals where x>0.7. The ferroelectric phase transition in SbSI-typ crystals and BiSb1-xSI crystals is caused by the phonon interaction's dependence on temperature, pressure and mixtureVytauto Didžiojo universitetasŠvietimo akademij

Photoelectron emission spectra of BiSCl crystal and molecular cluster

Vytauto Didžiojo universitetasŠvietimo akademij

Lattice dynamics of ferroelectric SbSBr crystal

The temperature dependence of phonon dispersion, total and partial phonon DOS of SbSBr crystal have been determined in paraelectric phase at T = 30 K and in ferroelectric phase at T = 11 K using FP—LAPW method in the framework of DFT along with the GGA approximation. Temperature dependence of total and partial phonon DOS for Sb, S and Br atoms where used for calculation of the vibration free energy of the unit cell Fvib and contribution from Sb, S and Br atoms to the free energy Fi,μ along c(z) —axis in quasiharmonic approximation in paraelectric and ferroelectric phases in temperature range from 11 K to 294 K. For investigation of softening effect nature of phonons along c(z) —axis the mean-squared displacements of Sb, S and Br atoms in x -, y -, z - direction have been calculated in quasiharmonic approximation in ferroelectric and paraelectric phasesVytauto Didžiojo universitetasŠvietimo akademij

Investigation of vibration spectrum ferroelectric semiconductor SbSBr nanowire

The temperature dependence of vibration spectra of one SbSBr chain (nanowire) in the direction of the c(z) – axis have been calculated in quasiharmonic approximation by diagonalization of dynamical matrix. The vibration frequencies in the direction of c(z) – axis have been derived by fitting of the experimental low – frequency ωs 2 of soft infrared (IR) mode of bulk – size SbSBr with theoretical quasiharmonic low - frequency ω2 of SbSBr nanowires. In this work the nature of anharmonism and temperature dependence of force constants between atoms in SbSBr crystal along c(z) – axis have been discussed. The anharmonism of all soft (at BZ k = 0) modes have been created by the interaction between phononsVytauto Didžiojo universitetasŠvietimo akademij

Investigation of the optical properties of SbSeBr

Vytauto Didžiojo universitetasŠvietimo akademij