Hindawi Publishing Corporation Advances in Physical Chemistry Volume 2013, Article ID 578686, 5 pages http://dx.doi.org/10.1155/2013/578686 Research Article The Lattice Compatibility Theory LCT: Physical and Chemical Arguments from the Growth Behavior of Doped Compounds in terms of Bandgap Distortion and Magnetic Effects K. Boubaker Ecole´ Superieure´ de Sciences et Techniques de Tunis (ESSTT), Universite´ de Tunis, 63 Rue Sidi Jabeur, Mahdia 5100, Tunisia Correspondence should be addressed to K. Boubaker; [email protected] Received 21 January 2013; Revised 2 April 2013; Accepted 20 May 2013 Academic Editor: Kenneth Ruud Copyright © 2013 K. Boubaker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Physical and chemical arguments for the recently discussed materials-related Lattice Compatibility Theory are presented. The discussed arguments are based on some differences of Mn ionscorporation in kinetics inside some compounds. These differences have been evaluated and quantified in terms of alteration of bandgap edges, magnetic patterns, and Faraday effect. 1. Introduction In this study, a support to the Lattice Compatibility Theory LCT is presented in terms of alteration of bandgap Bismuth oxides are nanocrystalline, fluorite-type materials edges, magnetic patterns, and Faraday effect. The paper is which exhibit unexpected lattice expansion during doping organized in the following way. In Section 2,somerelevant stages. They are used in various domains, such as transparent experimental details along with main manganese-doping ceramic glass, microelectronics, sensor technology, optical features are presented. In Section 3,wepresentphysical coatings, surface acoustic wave devices, and gas sensing [1– parameters alteration analysis along with LCT principles. 9]. Bismuth ternary oxides, such as Bi12SiO20,Bi4Ge3O12,and Section 4 is the conclusion. Bi4Ti3O12,usuallyexhibithighoxideionicconductivityand hence can been used as high-efficiency electrolyte materials for several applications such as oxygen sensors and solid 2. Samples Elaboration and oxide fuel cells (SOFC) [7–10]. Bi4Ge3O12 (BGO, Bismuth Measurement Techniques germanate) is a high density scintillation inorganic oxide with cubiceulytitestructure.Itisusedindetectorsinparticle Bi4Ti3O12 (BTO), Bi12SiO20 (BSO), and Bi4Ge3O12 (BGO) physics, gamma pulse spectroscopy, aerospace physics, and compounds have been prepared using the polymeric precur- nuclear medicine. Bi4Ti3O12 (BTO, Bismuth titanate) is a sor and Czochralski [11–14] methods using titanium tetraiso- layeredAurivilliusphaseperovskiteferroelectriccompound propoxide, Bismuth acetate, Bi2O3,GeO2 and SiO2 as precur- ∘ having a Curie temperature of about 675 C. In its monoclinic sors. Complexation and pH adjustment were achieved using ferroelectric state, Bi4Ti3O12 has been pointed at as a good wet ethylene glycol and ammonium hydroxide, respectively. candidate for use in nonvolatile memories, thanks to its excel- Mn-doping has been achieved using manganese carbonate lent fatigue resistance during repeated polarization reversals MnCO3 and manganese oxide MnO2 in various proportions. under electrical solicitation. In some recent studies [11, 12], Static magnetization and field dependence of magne- manganese-doped bismuth oxides showed nearly 10 times tization were measured at different applied fields in the the ionic conductivity of zirconia despite a low stability in temperature range 2–350 K with a SQUID magnetometer reducing environments. (Quantum Design for 0–5 T field range). Measurements have 2 Advances in Physical Chemistry been carried out as guides to determine zero field cooling (ZFC) molar susceptibility. Density of states Verdet coefficient measurement within the visible Energy Conduction band spectral domain has been obtained using a Faraday rotator which consists of a solenoid wrapped around a transparent dielectric material, along with four symmetric coils which produce controlled AC magnetic fields. The control unit was Ec equipped with a “New Focus Model” 8702 PCB mountable Defects Intrinsic single-axis driver. levels Finally, X-ray diffraction analysis of all prepared com- pounds was performed by a copper-source diffractometer E (Analytical X Pert PROMPD), with the wavelength = 1.54056 A˚ while optical absorption spectra were measured on double-side polished parallel crystal plates using a SPM-2 Valence band ± monochromator within accuracy of 2nm. Wavevector 3. Results and Discussion Figure 1: Urbach tailing and localized states in presence of defects. 3.1. Mn-Doping Patterns in terms of Bandgap, Magnetization, and Faraday Effects. In order to understand bandgap edges alteration following doping agent insertion in host structures, Urbach energy has been determined, for doped and undoped samples through the equations 4 ℎ] 3.5 ln ( (ℎ])) = ln (0)+ , 3 −1 −1 (1) 2.5 [ (ℎ])] () =(ℎ]) ( ) =ℎ[ ( (]))] , ln 2 [ℎ]] ] ln 1.5 where (ℎ]) represents, for each sample, the experimentally 1 deduced optical absorption profile. 0.5 Urbach energy is a measure of the inhomogenoeus 0 disorder and atomic scale dispersion inside structures as it 2 2.2 2.4 2.6 2.8 3 indicates the width of the band tails of the localized states E (eV) in presence of defects (Figure 1). Its analytical formulation is deduced by taking into account three components: structural BSO BTO BGO disorder, carrier-phonon interaction, and carrier-impurity: Undoped Undoped Undoped Doped Doped Doped Carrier-phonon interaction Structural⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞ disorder ⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞ Figure 2: Plots of (ln (])) versus energy ℎ] (as guides for evaluat- 1 4224∗3 = + ing ). 2 9√32ℎ2 (2) ⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞Carrier-impurity the considered samples, saturation of the magnetisation was + coth ( ) 2 reachedbyapplyingmagneticfieldupto5T.Themagnetic moment value per unit formula obtained from magnetization with: Boltzmann constant, : lattice strain related with the saturation is in good agreement with the expected ones from structural disorder, :Debyetemperature,:Debye the stoichiometric formula. ∗ length, : Carrier effective mass, :impuritycharge,:elec- Faraday effect (or Faraday rotation effect) is a magneto- tron charge, :staticdielectricpermittivity,ℎ:Planck’scon- optical phenomenon which was revealed in the beginning stant, and , , :constants. of the last century by Michael Faraday [15–18]andwhich The width of the localized states (band tail energy or consists of an interaction between light and a magnetic field Urbach energy ) has been estimated from the slopes of the inside a given medium [18, 19]. It causes a rotation of the plane plots of ln (]) versus energy ℎ] (Figure 2). of polarization which is linearly proportional to the compo- Figure 3 reports the temperature-dependent zero field nent of the magnetic field in the direction of propagation. The cooling (ZFC) molar susceptibility mol for BTO-, BGO-, and Faraday effect is based on the notion of circular birefringence, BSO- doped samples. All the samples show clear transitions which causes a difference of propagation speed between left from a paramagnetic (P) to a ferromagnetic (F) state. For all and right circularly polarized waves. Advances in Physical Chemistry 3 30 Table 1: Values of Verdet coefficient for doped and undoped sam- ples. 25 Sample Verdet coefficient (a. u.) Undoped 0.052 ) 20 BSO −1 Mn-doped 0.039 mol · 15 Undoped 0.041 BTO Mn-doped 0.038 (emu 10 Undoped 0.053 mol BGO Mn-doped 0.047 5 0 890 pm 0 50 100 150 200 250 300 T(K) BSO:Mn BTO:Mn BGO:Mn Figure 3: Zero field cooling (ZFC) molar susceptibility versus tem- perature for the doped samples. BGO:Mn BSO:Mn BTO:Mn Bi Ti/Ge O 203 pm Intensity (a.u.) Intensity 768 pm 30 31 32 33 34 35 36 37 38 39 40 2 (∘) Figure 4: XRD diagrams of the prepared compounds. Bi O Faraday effect has been evaluated, for the obtained sam- Si ples, through the measurements of alterations of the Verdet coefficient within the visible spectral domain. This coeffi- Figure5:BTOandBGOlatticesstructure. cient [19] is deduced via the measurement of the polarisation rotating angle using the formula 1 the same way inside the three studied lattice structures (BSO, = (3) BGO, and BTO). The Lattice Compatibility Theory [20–23] tries to give a plausible understanding of this disparity start- with : applied magnetic field strength (in oersteds) and : ing from intrinsic doping-element lattice properties in com- light path length through the medium. parison to those of the host. In the studied materials, changes Verdet coefficient changes for doped and undoped sam- in the studied parameters have been associated to a Mn- ples have been gathered in Table 1. XRD diagrams are also doping-induced disorder in BSO matrices against a relative gathered in Figure 4. unaltered stability of both BGO and BTO. For explanation purposes main lattice constants of Mn intrinsic lattice have 3.2. Lattice Compatibility Theory LCT Fundaments and Analy- been compared to those of BSO, BGO, and BTO (Figure 5). sis. StabilityofMnionswithinhostmatrixdoesnotoccurin Consecutively,athoroughstudyofBSOstructuresrevealeda 4 Advances in Physical Chemistry between doping agent intrinsic lattice and those of the host.” The many principles of this theory have been judged in good agreement with results published in the recent literature [17–23]. 4. Conclusion The present study tries to give