e-book Disorder and Order in the Solid State: Concepts and Devices

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The phase diagram was determined using the volume fraction of the particle, the surface charge density of the particle, and the salt concentration as experimental variables. With increasing charge density, the liquid state first became a solid state, and then a reentrant solid-to-liquid phase transition was observed. The reentrant transition with increasing charge density has been previously reported for dispersions of ionic silica, which have relatively large particle-size polydispersity. The solid regions for the present latex were much larger than those for the silica system.

The present study implies universality of the reentrant phase transition in charged colloidal systems, although the particle-size polydispersity affects the phase behavior in a quantitative manner.

Solid Polymer Electrolytes—Structure and Mechanism of Ion Transport

The reentrant transition could not be explained by the numerical simulation based on the Yukawa potential and renormalized charge concept. View Author Information. Cite this: Langmuir 19 8 Article Views Altmetric -. Citations Cited By. This article is cited by 14 publications.

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Full Revision of Solid state physics

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Tiffany White - Family Case. Get Free Consultation. Call us Monday-Friday, Nevertheless, only Sn-based ilmenite has this configuration indicating a big effect of ionic radius and interlayer distance of the FeO 6 clusters. The information obtained by these theoretical results demonstrates that the control of magnetic ordering in ilmenite materials is based on a complex relation between ionic radius and valence orbitals of the B-site non-magnetic metals.

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  4. The corundum ordered structure is most commonly called LiNbO 3 -type since this is the first material to present such crystalline phase. R3c materials are largely employed in development of memory devices, holographic data storage, electronic, electro-optical and optical devices, photo-induced devices and photocatalytic application due to a unique set of electronic, optical and ferroelectric properties usually observed for these materials.

    The first work on LiNbO 3 LNO structure were reported in and discuss this new structure as a ilmenite type; [ 33 ] however, in such information were refuted by Bailey [ 34 , 35 ] that obtained results proving that, at room conditions, the LNO crystallizes in a R3c group instead of a R3 group characteristic of ilmenite. These features are the responsible for the high ferroelectric properties characteristic of this type of structure. Crystalline structures of R3c structure showing the alternation between B, A and vacancies along z axis a , [AO6] and [BO6] octahedra within structure b and magnetic coupling constant J for R3c structures c.

    The magnetism in this structure arises from unpaired electron from atoms occupying A or B sites within structure. At general, the magnetism in Solid State materials can be successfully described by Direct or Indirect interactions, Exchange interactions and Super Exchange interactions or Goodenough-Kanamori-Anderson GKA Rule; all of them, considers the unit cell magnetic resultant to determine the magnetism.

    However, the structural disorder makes such approaches not enough to predict the magnetism in R3c structures.

    Solid-state physics: Consider the 'anticrystal'

    Thus, for materials where the value of the equation is less than 1. Moreover, the theoretical investigation also provides information regarding to electronic levels of magnetic cations in XNiO 3 and NiXO 3. Furthermore, projected Density of States DOS clarifies why magnetic ordering is changed from chemical modifications. The gray region represents the broken on degeneration of t2g energy levels. However, how to understand the origin of the FM ordering in these materials? The existence of the FM ordering in materials is dependent on the spin orientation being in the same direction on all magnetic clusters.

    Moreover, magnetic LNO-type materials have attracted the interest of materials scientist around the world in the last years as promising alternatives as smart and functional materials, mainly as multiferroic MF materials. The multiferroism consists on the coupling between magnetic ordering and some ferroic property in the same crystalline phase, but the main form of multiferroism is called of magnetoelectric ME coupling and are obtained by coupling between the magnetic ordering and ferroelectric properties. Consequently, electric polarization can be induced by a magnetic field or vice-versa.

    The ME coupling was first reported in the first years of s decade; thus, the study of this effect keep stable until that, in , a strong coupling between ferroelectric and magnetic properties was observed for TbMnO 3 and TbMn 2 O 5 materials as well as a high ferroelectricity for BiFeO 3 BFO films.

    Thenceforth, the study of MF materials increases drastically so that a fast search on Web of Science indicates at least manuscripts focused in this class of material only in The investigation of multiferroic materials aims its application at development of several devices such as actuators, magnetic readers, sensors, tunneling and data storage devices. Moreover, MF materials are also potential alternatives for spintronics. The main representative of this class is the BFO; this material exhibits antiferromagnetic ordering as well as Magnetoelectric coupling at room conditions allied to a unique set of electronic, optical, magnetic and ferroelectric properties.

    Even that many multiferroic materials are currently known, the development of MF material is this kind of material is delayed by crystalline structure and low Curie temperature T C ; the first due to the fact that only 13 symmetry groups are able to exhibit multiferroic coupling, while the last makes its application impossible in technological purposes [ 42 ]. Historically, the investigation of new materials aiming technological applications was a hard task that needed a long time of study. In this period, the theoretical-computational method was seen only as tool to study of materials already discovered.

    Front of the fact that the technological advance is extremely dependent on development of new materials, theoretical methods helped materials chemists and physicist on development materials at higher speed. Ever since, theoretical methods based on quantum mechanical simulations are an important tool to evaluate material properties, mainly at the molecular level [ 43 ]. Another factor responsible for wide use of this theory is the high versatility, once presents good results to investigation of magnetic materials, semiconductors, proteins, organic compounds and others [ 45 ].

    Several computational approaches can be applied to evaluation of materials properties; for instance: Molecular Dynamics MD , ab initio methods and Semi-Empirical Methods. In turn, DFT assumes that the system Total Energy is a unique functional of electronic density; this methodology can be simplified in two postulates: [ 46 ]. Any try function for electronic density will have energy greater or equal than the ground state energy for a real system.

    Although this similarity was observed, the DFT shows a highest precision and computational cost in relation to HF simulations due to smaller number of variable.

    2 editions of this work

    The HF and Semi-Empirical methods employ a number of variables in the 4n order, where n refers to the number of electrons in the system; whereas, the DFT is dependent on three variables [ 43 , 44 ]. The DFT formulism was proposed by Kohn and Shan KS in and consists in two equations applied on two different systems; such systems consider that there are no or there are interactions between electrons, respectively. The results for both systems show a significant difference of energy between then, and, aiming to correct this difference, the Exchange-correlation Term E XC was inserted in DFT proposed.

    Introduction to Solid State Ionics: Phenomenology and Applications - CRC Press Book

    The E XC is the sum of kinetic and potential energy difference between both systems. The description of E XC terms changes according to employed exchange-correlation functional and, hence, the choice of a functional has a giant effect on materials properties evaluation, as offering better results as offering a reduction in computational cost. The DFT is widely used on materials modeling since offers an excellent relation time x efficiency, as denoted by results precision on prevision of materials properties in a short time.

    For instance, a DFT methodology provides thermodynamic properties for bulk or surfaces of materials directly or using some additional approach as Berry Phase [ 47 , 48 ] or Bulk Modulus [ 49 , 50 ]. In turn, in Solid State materials the magnetic interactions are usually described by the Heisenberg Hamiltonian; however, in computer simulations this approach cannot be used because later determinant is not an eigenstate of such Hamiltonian. Thus, it is necessary the application of the Ising model which possibilities the evaluation of J magnetic coupling constant and ground-state magnetic ordering for simple and complex magnetic structure since using the energy difference between AFM and FM magnetic states since the unpaired electrons are well defined in the model Eq.

    The Ising Model is described by Eq. Both Eqs. The application of Ising Model was performed after the structural optimization of magnetic materials and requires that the spin orientation of unpaired electrons is well defined in the model. The Ising Model is described by Eqs. Plus, in materials with more than one magnetic and not reproductive site, the Ising model should be applied to each magnetic ordering and thus, applied to ground-state model.

    The Ising Model methodology to prevision of magnetic properties of Solid State materials was employed by Ribeiro and coauthors [ 51 ], Chartier and coauthors [ 52 ], Feng and Harrison [ 53 ] and Lacerda and de Lazaro [ 39 ] to investigate materials and different crystalline structures proving the efficiency of this approach.