Calcium Copper Titanate
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Calcium Copper Titanate
Calcium copper titanate (also abbreviated CCTO, for calcium copper titanium oxide) is an inorganic compound with the formula CaCu3Ti4O12. It is noteworthy for its extremely large dielectric constant (effective relative permittivity) of in excess of 10,000 at room temperature. History CCTO was first synthesized in 1967 by Alfred Deschanvres and his coworkers. While the structural features were known, no physical properties had been measured. In 2000, Mas Subramanian and his colleagues at DuPont Central R&D discovered that CCTO displayed a dielectric constant greater than 10,000, compared to the normal dielectric SrTiO3, which has a constant of 300 at room temperature. Since then, it has found widespread usage in capacitor applications. Synthesis and structure Most compounds which form this crystal structure are made under high-pressure conditions. Pure CCTO, however, can be easily synthesized by standard solid state methods via intimate mixtures of the metal carbonate a ...
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Cubic Crystal System
In crystallography, the cubic (or isometric) crystal system is a crystal system where the Crystal_structure#Unit_cell, unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called Close-packing_of_equal_spheres, ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive_cell, primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one Lattice_(group), lattice point on each corner of the cube; this means each simple cubic unit cell has in total one latt ...
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Perovskite
Perovskite (pronunciation: ) is a calcium titanium oxide mineral composed of calcium titanate (chemical formula ). Its name is also applied to the class of compounds which have the same type of crystal structure as (XIIA2+VIB4+X2−3), known as the perovskite structure. Many different cations can be embedded in this structure, allowing the development of diverse engineered materials. History The mineral was discovered in the Ural Mountains of Russia by Gustav Rose in 1839 and is named after Russian mineralogist Lev Perovski (1792–1856). Perovskite's notable crystal structure was first described by Victor Goldschmidt in 1926 in his work on tolerance factors. The crystal structure was later published in 1945 from X-ray diffraction data on barium titanate by Helen Dick Megaw. Occurrence Found in the Earth's mantle, perovskite's occurrence at Khibina Massif is restricted to the silica under-saturated ultramafic rocks and foidolites, due to the instability in a paragenesis ...
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University Of Sheffield
, mottoeng = To discover the causes of things , established = – University of SheffieldPredecessor institutions: – Sheffield Medical School – Firth College – Sheffield Technical School – University College of Sheffield , type = Public research university , academic_staff = 5,670 (2020) - including academic atypical staff , administrative_staff = , chancellor = Lady Justice Rafferty , vice_chancellor = Koen Lamberts , students = () , undergrad = () , postgrad = () , endowment = £46.7 million (2021) , budget = £741.0 million (2020–21) , city = Sheffield , state = South Yorkshire , country = England , coor = , campus = Urban , colours = Black & gold , affiliations = Russell Group WUN ACUN8 Group White Rose Sutton 30EQUISAMBAUniversities UK , website = , logo = The University of Sheffield (informally Sheffield University or TUOS) is a public research university in Sheffield, South Yorkshire, England. Its history traces back to the f ...
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Crystal Structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of Three-dimensional space (mathematics), three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive Translation (geometry), translation of the unit cell along its principal axes. The translation vectors define the nodes of the Bravais lattice. The lengths of the principal axes, or edges, of the unit cell and the angles between them are the lattice constants, also called ''lattice parameters'' or ''cell parameters''. The symmetry properties of the crystal are described by the con ...
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Grain Boundary
In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship. High and low angle boundaries It is convenient to categorize grain boundaries according to the extent of misorientation between the two grains. ''Low-angle grain boundaries'' (''LAGB'') or ''subgrain boundaries'' are those with a misorientation less than about 15 degrees. Generally speaking they are composed of a ...
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Dielectric Loss
Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle ''δ'' or the corresponding loss tangent tan ''δ''. Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart. Electromagnetic field perspective For time varying electromagnetic fields, the electromagnetic energy is typically viewed as waves propagating either through free space, in a transmission line, in a microstrip line, or through a waveguide. Dielectrics are often used in all of these environments to mechanically support electrical conductors and keep them at a fixed separation, or to provide a barrier between different gas pressures yet still transmit electromagnetic power. Maxwell’s equations are solved for the electric and magnetic field components of the propagating waves ...
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Clausius–Mossotti Relation
The Clausius–Mossotti relation expresses the dielectric constant (relative permittivity, ''ε''r) of a material in terms of the atomic polarizability, α, of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof. It is named after Ottaviano-Fabrizio Mossotti and Rudolf Clausius. It is equivalent to the Lorentz–Lorenz equation. It may be expressed as: \frac = \frac where *\varepsilon_r = \varepsilon/\varepsilon_0 is the dielectric constant of the material, which for non-magnetic materials is equal to n^2 where n is the refractive index *\varepsilon_0 is the permittivity of free space *N is the number density of the molecules (number per cubic meter), and *\alpha is the molecular polarizability in SI-units (C·m2/V). In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by ''i'' ...
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Jahn–Teller Effect
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937.Bunker, Philip R.; Jensen, Per (1998) ''Molecular Symmetry and Spectroscopy'' (2nd ed.). NRC Research Press, Ottaw/ref> Simplified overview The Jahn–Teller effect, sometimes also referred to as Jahn–Teller distortion, describes the geometrical distortion of molecules and ions that result from certain electron configurations. The Jahn–Teller theorem essentially states that any non-linear molecule with a spatially degenerate energy level, degenerate electronic ground state will undergo a geometrical distortion that removes th ...
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Square Planar Molecular Geometry
The square planar molecular geometry in chemistry describes the stereochemistry (spatial arrangement of atoms) that is adopted by certain chemical compounds. As the name suggests, molecules of this geometry have their atoms positioned at the corners. Examples Numerous compounds adopt this geometry, examples being especially numerous for transition metal complexes. The noble gas compound XeF4 adopts this structure as predicted by VSEPR theory. The geometry is prevalent for transition metal complexes with d8 configuration, which includes Rh(I), Ir(I), Pd(II), Pt(II), and Au(III). Notable examples include the anticancer drugs cisplatin tCl2(NH3)2and carboplatin. Many homogeneous catalysts are square planar in their resting state, such as Wilkinson's catalyst and Crabtree's catalyst. Other examples include Vaska's complex and Zeise's salt. Certain ligands (such as porphyrins) stabilize this geometry. Splitting of d-orbitals A general d-orbital splitting diagram for square planar ...
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Rhenium Trioxide
Rhenium trioxide or rhenium(VI) oxide is an inorganic compound with the formula ReO3. It is a red solid with a metallic lustre that resembles copper in appearance. It is the only stable trioxide of the Group 7 elements ( Mn, Tc, Re). Preparation and structure Rhenium trioxide can be formed by reducing rhenium(VII) oxide with carbon monoxide at 200 °C or elemental rhenium at 400 °C. :Re2O7 + CO → 2 ReO3 + CO2 :3 Re2O7 + Re → 7 ReO3 Re2O7 can also be reduced with dioxane. Rhenium trioxide crystallizes with a primitive cubic unit cell, with a lattice parameter of 3.742 Å (374.2 pm). The structure of ReO3 is similar to that of perovskite (ABO3), without the large A cation at the centre of the unit cell. Each rhenium center is surrounded by an octahedron defined by six oxygen centers. These octahedra share corners to form the 3-dimensional structure. The coordination number of O is 2, because each oxygen atom has 2 neighbouring Re atoms., p. 1 ...
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Solid-state Reaction Route
The solid-state reaction route is the most widely used method for the preparation of polycrystalline solids from a mixture of solid starting materials. Solids do not react together at room temperature over normal time scales and it is necessary to heat them to much higher temperatures, often to 1000 to 1500 °C, in order for the reaction to occur at an appreciable rate. The factors on which the feasibility and rate of a solid state reaction depend include, reaction conditions, structural properties of the reactants, surface area of the solids, their reactivity and the thermodynamic free energy change associated with the reaction. Outline of the experimental procedure Reagents These are the solid reactants from which it is proposed to prepare a solid crystalline compound. The selection of reactant chemicals depends on the reaction conditions and expected nature of the product. The reactants are dried thoroughly prior to weighing. As increase in surface area enhances the reacti ...
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