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Born–Landé Equation
The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term. :E =- \frac\left(1-\frac\right) where: *''N''A = Avogadro constant; *''M'' = Madelung constant, relating to the geometry of the crystal; *''z''+ = numeric charge number of cation *''z''− = numeric charge number of anion *''e'' = elementary charge, 1.6022 C *''ε''0 = permittivity of free space *:4π''ε''0 = 1.112 C2/(J·m) *''r''0 = distance between closest cation +ve & anion -ve *''n'' = Born exponent, typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically. *E = Lattice energy is expressed by 'E' . Derivation The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Energy
In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ionic solids. The size of the lattice energy is connected to many other physical properties including solubility, hardness, and volatility. Since it generally cannot be measured directly, the lattice energy is usually deduced from experimental data via the Born–Haber cycle. Lattice energy and lattice enthalpy The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt (NaCl) and sphalerite (ZnS), where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction : Na+ (g) + Cl− (g) → NaCl (s) which amounts to −786 kJ/mol. Some chemistry textbooks as well as the widely used CRC Handbook of Chemistry and P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb
The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary charges, , (about ). Name and history By 1878, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb. In 1881, the International Electrical Congress, now the International Electrotechnical Commission (IEC), approved the volt as the unit for electromotive force, the ampere as the unit for electric current, and the coulomb as the unit of electric charge. At that time, the volt was defined as the potential difference .e., what is nowadays called the "voltage (difference)"across a conductor when a current of one ampere dissipates one watt of power. The coulomb (later "absolute coulomb" or "abcoulomb" for disambiguation) was part of the EMU system of units. The "international coulo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Chemistry
Solid-state chemistry, also sometimes referred as materials chemistry, is the study of the synthesis, structure, and properties of solid phase materials, particularly, but not necessarily exclusively of, non-molecular solids. It therefore has a strong overlap with solid-state physics, mineralogy, crystallography, ceramics, metallurgy, thermodynamics, materials science and electronics with a focus on the synthesis of novel materials and their characterisation. Solids can be classified as crystalline or amorphous on basis of the nature of order present in the arrangement of their constituent particles. History Because of its direct relevance to products of commerce, solid state inorganic chemistry has been strongly driven by technology. Progress in the field has often been fueled by the demands of industry, sometimes in collaboration with academia. Applications discovered in the 20th century include zeolite and platinum-based catalysts for petroleum processing in the 1950s, high-pur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born–Mayer Equation
The Born–Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound. It is a refinement of the Born–Landé equation by using an improved repulsion term. :E =- \frac\left(1-\frac\right) where: *''N''A = Avogadro constant; *''M'' = Madelung constant, relating to the geometry of the crystal; *''z''+ = charge number of cation *''z''− = charge number of anion *''e'' = elementary charge, 1.6022 C *''ε''0 = permittivity of free space *:4''ε''0 = 1.112 C2/(J·m) *''r''0 = distance to closest ion *''ρ'' = a constant dependent on the compressibility of the crystal; 30 pm works well for all alkali metal halides See also *Born–Landé equation *Kapustinskii equation The Kapustinskii equation calculates the lattice energy ''UL'' for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in 1956. :U_ = \cdot \frac \cdot \big ... Refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kapustinskii Equation
The Kapustinskii equation calculates the lattice energy ''UL'' for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in 1956. :U_ = \cdot \frac \cdot \biggl( 1 - \frac \biggr) : The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SO) or phosphate (PO). Derivation from the Born–Landé equation Kapustinskii originally proposed the following simpler form, which he faulted as "associated with antiquated concepts of the character of repulsion forces". :U_ = \cdot \frac Here, ''K''' = 1.079 J·m·mol−1. This form of the Kapustinskii equation may be derived as an approximation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erwin Madelung
Erwin Madelung (18 May 1881 – 1 August 1972) was a German physicist. He was born in 1881 in Bonn. His father was the surgeon Otto Wilhelm Madelung. He earned a doctorate in 1905 from the University of Göttingen, specializing in crystal structure, and eventually became a professor. It was during this time he developed the Madelung constant, which characterizes the net electrostatic effects of all ions in a crystal lattice, and is used to determine the energy of one ion. In 1921 he succeeded Max Born as the Chair of Theoretical Physics at the Goethe University Frankfurt, which he held until his retirement in 1949. He specialized in atomic physics and quantum mechanics, and it was during this time he developed the Madelung equations, an alternative form of the Schrödinger equation. He is also known for the Madelung rule, which states that atomic orbitals are filled in order of increasing n + l quantum numbers. Publications * ''Magnetisierung durch schnell verlaufende Stromvorg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. In its simple form, the compressibility \kappa (denoted in some fields) may be expressed as :\beta =-\frac\frac, where is volume and is pressure. The choice to define compressibility as the negative of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus. Definition The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal. Accordingly, isothermal compressibility is defined: :\beta_T=-\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permittivity Of Free Space
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: : (farads per meter), with a relative uncertainty of It is a measure of how dense of an electric field is "permitted" to form in response to electric charges, and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: :F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/4 \pi \varepsilon_0 (known as the Coulomb constant, ''k''e) is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as e = coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from bla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ionic Compound
In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged ions called anions. These can be simple ions such as the sodium (Na+) and chloride (Cl−) in sodium chloride, or polyatomic species such as the ammonium () and carbonate () ions in ammonium carbonate. Individual ions within an ionic compound usually have multiple nearest neighbours, so are not considered to be part of molecules, but instead part of a continuous three-dimensional network. Ionic compounds usually form crystalline structures when solid. Ionic compounds containing basic ions hydroxide (OH−) or oxide (O2−) are classified as bases. Ionic compounds without these ions are also known as salts and can be formed by acid–base reactions. Ionic compounds can also be produced from their constituent ions by evaporation of their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Madelung Constant
The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. It is named after Erwin Madelung, a German physicist. Because the anions and cations in an ionic solid attract each other by virtue of their opposing charges, separating the ions requires a certain amount of energy. This energy must be given to the system in order to break the anion–cation bonds. The energy required to break these bonds for one mole of an ionic solid under standard conditions is the lattice energy. Formal expression The Madelung constant allows for the calculation of the electric potential V_i of all ions of the lattice felt by the ion at position r_i :V_i = \frac \sum_ \frac\,\! where r_ = , r_i-r_j, is the distance between the i^ and the j^ ion. In addition, :z_j = number of charges of the j^ ion :e= 1.6022 C :4\pi \epsilon_0= . If the distances r_ are normalized to the nearest neighbor distance r_0, the potent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Avogadro Constant
The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of . It is named after the Italian scientist Amedeo Avogadro by Stanislao Cannizzaro, who explained this number four years after Avogadro's death while at the Karlsruhe Congress in 1860. The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted or , which is the number of particles that are contained in one mole, exactly . The Avogadro number is the approximate number of nucleons (protons or neutrons) in one gram of ordinary matter. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is approximately the number of nucleons in one cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
