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Energy change upon the formation of one mole of ionic solid
In chemistry, the lattice energy is the energy change (released) upon formation of one mole of a crystalline compound from its infinitely separated constituents
Lattice_energy
Formula for lattice energy
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
Born–Landé_equation
Strength of a chemical bond
effect on their bond energy. The extent of this effect is described by the compound's lattice energy, where a more negative lattice energy corresponds to a
Bond_energy
Chemical bonding involving attraction between ions
other releases (lattice) energy and, thus, lowers the overall energy of the system. Ionic bonding will occur only if the overall energy change for the
Ionic_bonding
Energy released by one mole of ions in a hydration reaction
crystalline solid comprises the hydration energy. If the hydration energy is greater than the lattice energy, then the enthalpy of solution is negative
Hydration_energy
Formula for lattice energy
The Kapustinskii equation calculates the lattice energy UL for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli
Kapustinskii_equation
Approach to analyzing reaction energies
a means of calculating lattice energy (or more precisely enthalpy), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy
Born–Haber_cycle
Primitive cell in the reciprocal space lattice of crystals
In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones
Brillouin_zone
Chemical compound involving ionic bonding
a reasonable form is assumed for the additional repulsive energy, the total lattice energy can be modelled using the Born–Landé equation, the Born–Mayer
Salt_(chemistry)
Constant in crystallography
bonds for one mole of an ionic solid under standard conditions is the lattice energy. The Madelung constant allows for the calculation of the electric potential
Madelung_constant
Fourier transform of a real-space lattice, important in solid-state physics
electron diffraction as well as the energies of electrons in a solid. It emerges from the Fourier transform of the lattice associated with the arrangement
Reciprocal_lattice
Energy range in a solid where no electron states exist
the lattice phonons and the free electrons and holes will also affect the band gap to a smaller extent. The relationship between band gap energy and temperature
Band_gap
Physical quantity
amount of heat (known as the lattice energy) to the surroundings. Although heat is "wasted" energy for a specific energy transfer (see: waste heat), it
Energy
Transition from solid to gas without melting
assumed. Δ H sublimation = − U lattice energy − 2 R T {\displaystyle \Delta H_{\text{sublimation}}=-U_{\text{lattice energy}}-2RT} Dye-sub printing is a
Sublimation (phase transition)
Sublimation_(phase_transition)
German chemist (1868–1934)
Born, proposed the Born–Haber cycle as a method for evaluating the lattice energy of an ionic solid. Haber, a known German nationalist, is also considered
Fritz_Haber
Association of molecules of a solvent with molecules or ions of a solute
hydration. Solubility of solid compounds depends on a competition between lattice energy and solvation, including entropy effects related to changes in the solvent
Solvation
Mathematical model of ferromagnetism in statistical mechanics
maximum difference in energy would be 4J. Let c represent the lattice coordination number; the number of nearest neighbors that any lattice site has. We assume
Ising_model
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
Born–Mayer_equation
Topics referred to by the same term
3166-2:IT code LE), Italy London Eye, a ferris wheel on the Thames Lattice energy, the energy of formation of a crystal from infinitely-separated ions Lewis
LE
Australian energy company
2017, Origin sold its subsidiary Lattice Energy and its conventional upstream oil and gas business to Beach Energy for $1,585 million. Australia Pacific
Origin_Energy
Quasiparticle of mechanical vibrations
by a potential energy function V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all
Phonon
Inorganic compound group
propyne and 4 equivalents of butyllithium in hexanes. Due to its higher lattice energy, Mg2C3 is much more stable than Li4C3. For example, only the latter
Carbide
Class of computational fluid dynamics methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is
Lattice_Boltzmann_methods
Chemical rule of thumb
positively-charged Na+ and negatively-charged Cl− ions, which releases a 8.12 eV lattice energy. By contrast, any further electrons removed from Na would reside in
Octet_rule
derived the Kapustinskii equation that allows an estimation of the lattice energy of an ionic crystal. Kapustinskii was born in Zhytomyr, Russian Empire
Anatoli_Kapustinskii
Change in enthalpy from dissolving a substance
property Enthalpy of mixing Heat of dilution Heat of melting Hydration energy Lattice energy Law of dilution Solvation Thermodynamic activity Solubility equilibrium
Enthalpy_change_of_solution
Quantum chromodynamics on a lattice
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge
Lattice_QCD
Describes the range of energies of an electron within the solid
orbitals with different energies. Similarly, if a large number N of identical atoms come together to form a solid, such as a crystal lattice, the atoms' atomic
Electronic_band_structure
Atomic-scale structure formed through the Stark shift by opposing beams of light
the optical lattice may move due to quantum tunneling, even if the potential well depth of the lattice points exceeds the kinetic energy of the atoms
Optical_lattice
Energy needed to remove an electron
concept describing the energy released by adding an electron to a neutral atom or molecule. Lattice energy, a measure of the energy released when ions are
Ionization_energy
Change of enthalpy during the formation of a compound from its elements
experimentally, but the lattice energy cannot be measured directly. The equation is therefore rearranged to evaluate the lattice energy: − U L = Δ H sub +
Standard enthalpy of formation
Standard_enthalpy_of_formation
Group of highly reactive chemical elements
all the energy released from the formation of an alkali metal nitride is from the lattice energy of the alkali metal nitride. The lattice energy is maximised
Alkali_metal
Any measure of hardness based on scratch resistance
diamond bort. There is a linear relationship between cohesive energy density (lattice energy per volume) and Wooddell wear resistance, occurring between
Scratch_hardness
Distortion of the periodic lattice of a one-dimensional crystal
an electron in a 1-D crystal with lattice spacing a {\displaystyle a} . The periodicity of the crystal creates energy band gaps in the ϵ − k {\displaystyle
Peierls_transition
Australian Oil & Gas producing company
91 (Beach 100%). In September 2017, Beach Energy announced it would acquire Lattice Energy from Origin Energy for $1.585 billion, significantly increasing
Beach_Energy
Salt in the liquid state
have high lattice energies, manifested in high melting points. Some salts, especially those with organic cations, have low lattice energies and thus are
Ionic_liquid
grind size as excess energy goes into lattice energy. Crystalline magnesium oxide, or periclase, has a calculated lattice energy of 3795 kJ mol-1 which
Reactive_magnesia
Theoretical electronic band structure model in which the potential is periodic and weak
irregular lattice, in which the potential is not even periodic. The empty lattice approximation describes a number of properties of energy dispersion
Empty_lattice_approximation
Physical phenomenon
higher energy, non-equilibrium state to thermodynamic equilibrium with its surroundings (the "lattice"). It is characterized by the spin–lattice relaxation
Spin–lattice_relaxation
Iron (II) disulfide mineral
Madelung constants and has to be included in the calculation of the lattice energy by using a generalised Born–Haber cycle. This reflects the fact that
Pyrite
When the ratio of reactants to products of a chemical reaction is constant with time
dimethylglyoxime, (dmgH2): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of solvation of the molecule Ni(dmgH)2
Chemical_equilibrium
Town in Victoria, Australia
the Otway Basin. It was owned by Lattice Energy, a subsidiary of Origin Energy. Origin sold Lattice to Beach Energy in 2017. Forty percent of the Victorian
Waarre
Chemical compound
this polymorph. Both ions are six-coordinate in this arrangement. The lattice energy of this polymorph is only 3.2 kJ/mol less than the following structure's
Rubidium_chloride
Lattice proteins are highly simplified models of protein-like heteropolymer chains on lattice conformational space which are used to investigate protein
Lattice_protein
Thermodynamic law in chemistry
or Electron affinities using a Born–Haber cycle with a theoretical lattice energy. Chemistry portal Thermochemistry Thermodynamics "5.6: Hess's Law".
Hess's_law
Solvent interface of a solute
transport number Ionic radius Water model Poisson–Boltzmann equation Hydration energy Solvation Glueckauf, E. (1955). "The influence of ionic hydration on activity
Solvation_shell
Model in Quantum Physics
mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the
Particle in a one-dimensional lattice
Particle_in_a_one-dimensional_lattice
Chemical element with atomic number 20 (Ca)
those of the hypothetical MX. This occurs because of the much greater lattice energy afforded by the more highly charged Ca2+ cation compared to the hypothetical
Calcium
Phenomenon of deformation due to structural stress
be applied to overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site. The applied stress to
Yield_(engineering)
Standard enthalpy change when a chemical bond is cleaved by homolysis
dissociation energies for common organic compounds are shown below. Bond energy Electronegativity Ionization energy Electron affinity Lattice energy IUPAC,
Bond_dissociation_energy
where Elat is the static internal lattice energy, Uvib is the internal vibrational energy of the lattice, or the energy of the phonon system, T is the absolute
Quasi-harmonic_approximation
Chemical element with atomic number 14 (Si)
specifically in a diamond cubic crystal lattice (space group 227). It thus has a high melting point of 1414 °C, as a lot of energy is required to break the strong
Silicon
Salt or ester of carbonic acid
are far more soluble. This difference is related to the disparate lattice energies of solids composed of mono- vs dianions, as well as mono- vs dications
Carbonate
Enthalpy change when a substance melts
(Estimation of the heat of fusion from molecular structure) Latent heat Lattice energy Heat of dilution Atkins & Jones 2008, p. 236. Ott & Boerio-Goates 2000
Enthalpy_of_fusion
Substance whose dissolved ions conduct electricity
PMMA, PAN, polyphosphazenes, siloxanes, etc.) and a salt with low lattice energy. In order to increase the mechanical strength and conductivity of such
Electrolyte
Rules to predict ionic compounds' crystal structures
anions which form a polyhedron. Ions assemble into a crystal lattice when the lattice energy released by collective packing exceeds the stabilization of
Pauling's_rules
Substance that can explode
and thus they are not thermodynamically stabilized by a high ionic-lattice energy. Furthermore, they generally have positive enthalpies of formation,
Explosive
Alloy
47. To obtain lattice matching at the growth temperature, it is necessary to increase the GaAs mole fraction to 0.48. The bandgap energy of GaInAs can
Indium_gallium_arsenide
Australian-based art collector and philanthropist
Mordant also worked on another energy-related deal in 2019, advising on the acquisition of Lattice Energy by Beach Energy. The agreed acquisition price
Simon_Mordant
Measure of a substance's tendency towards ionic conduction
device for electric vehicles while developing the sodium–sulfur battery. Lattice energy Fast ion conductor NASICON Richard Turton. (2000).The Physics of Solids
Ionic conductivity (solid state)
Ionic_conductivity_(solid_state)
Physical model defined on a lattice
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as
Lattice_model_(physics)
Energy collected from renewable resources
Renewable energy (also called green energy) is energy made from renewable natural resources that are replenished on a human timescale. The most widely
Renewable_energy
Light energy absorbance and re-emission
phosphorescence occurs when an atom absorbs a high-energy photon and an electron becomes trapped in a defect in the lattice of the crystalline or amorphous material
Phosphorescence
Type of a chemical reaction
counterions. The choice of reactants is guided by a solubility chart or lattice energy. HSAB theory can also be used to predict the products of a metathesis
Salt_metathesis_reaction
help stabilize the polyhalogen ions formed in the solid state from lattice energy considerations, as the packing efficiency increases. The polyhalogen
Polyhalogen_ions
Designing solid structures with tailored properties
to calculate the lattice energies precisely. Apart from the ability of predicting crystal structures, CSP also gives computed energy landscapes of crystal
Crystal_engineering
Concept in physics
photon energy is equal to the energy difference between the two electronic states ( E 1 − E 0 {\displaystyle E_{1}-E_{0}} ) plus three quanta of lattice mode
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
through lutetium. lattice The unique geometric arrangement of atoms or molecules in a crystalline liquid or solid. lattice energy The energy released upon
Glossary_of_chemistry_terms
Chemical compound
Holger Kalkhof: Crystal Engineering on Industrial Diaryl Pigments Using Lattice Energy Minimizations and X-ray Powder Diffraction. In: The Journal of Physical
Pigment_Yellow_14
Energy needed to dislocate an atom within a solid lattice
displacement energy (Td) is the minimum kinetic energy that an atom in a solid needs to be permanently displaced from its site in the lattice to a defect
Threshold_displacement_energy
Chemical compound
needed] The electron affinity energy of chlorine tetroxide can be figured out using the Born–Haber cycle and the lattice energy data of perchlorates. It is
Chlorine_tetroxide
Contribution to magnetic exchange interaction
because the systems tend to enhance the magnetic interaction energy at the cost of lattice energy. This mechanism is called "inverse Dzyaloshinskii–Moriya
Antisymmetric_exchange
Ion
4-Triazolium-, and Tetrazolium-Based Energetic Salts from Isodesmic and Lattice Energy Calculations". The Journal of Physical Chemistry B. 111 (18): 4788–4800
Imidazolate
Compound of nitrogen with a formal oxidation state of –3
carbides, nitrides are often refractory materials owing to their high lattice energy, which reflects the strong bonding of "N3−" to metal cation(s). Thus
Nitride
Solid (crystalline) phase of electrons
and form a lattice if the electron density is less than a critical value. This is because the potential energy dominates the kinetic energy at low densities
Wigner_crystal
Chemical compound
Holger Kalkhof: Crystal Engineering on Industrial Diaryl Pigments Using Lattice Energy Minimizations and X-ray Powder Diffraction. In: The Journal of Physical
Pigment_Yellow_83
Theory of quantum gauge fields on a lattice
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important
Lattice_gauge_theory
Type of nuclear fusion
Lattice confinement fusion (LCF) is a type of nuclear fusion in which deuteron-saturated metals are exposed to high energy photons or ion beams avoiding
Lattice_confinement_fusion
Chemical compound
which decreases with an increase in temperature. La2O3 has the lowest lattice energy of the rare-earth oxides, with very high dielectric constant ε = 27
Lanthanum_oxide
Hypothetical type of nuclear reaction
excess energy into the host metal lattice prior to the intermediary's decay inexplicable by conventional understandings of momentum and energy transfer
Cold_fusion
Ordered arrangement of atoms, ions, or molecules in a crystalline material
the Bravais lattice. The lengths of principal axes/edges, of the unit cell and angles between them are lattice constants, also called lattice parameters
Crystal_structure
Microscopic theory of superconductivity
pairs of electrons known as Cooper pairs. These pairs move through the lattice without resistance. The theory is named after John Bardeen, Leon Cooper
BCS_theory
Group of chemicals
hydrocarbon backbone metal bis(trimethylsilyl)amide complexes have low lattice energies and are lipophilic. For this reason, they are soluble in a range of
Metal bis(trimethylsilyl)amides
Metal_bis(trimethylsilyl)amides
Freestanding framework tower
A lattice tower, or truss tower, is a freestanding vertical framework tower. This construction is widely used in transmission towers carrying high-voltage
Lattice_tower
Electron diffraction by reflection from surfaces
RHEED users can directly calculate the reciprocal lattice of the sample with a RHEED pattern, the energy of the incident electrons and the distance from
Reflection high-energy electron diffraction
Reflection_high-energy_electron_diffraction
Class of physical phenomena
two-dimensional lattice where every lattice node had one electron. If one electron was removed under specific conditions, the lattice's energy would be minimal
Magnetism
Scattering from arrays of atoms
scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between
Bragg's_law
Simplified model in condensed matter physics
tight-binding model, which only includes kinetic energy (a "hopping" term) and interactions with the atoms of the lattice (an "atomic" potential). When the interaction
Hubbard_model
Ability of a solid material to exist in more than one form or crystal structure
Most polymorphs of organic molecules only differ by a few kJ/mol in lattice energy. Approximately 50% of known polymorph pairs differ by less than 2 kJ/mol
Crystal_polymorphism
Chemical compound
1515/znb-2004-11-1207. S2CID 99733089. Brock, C. P. (1977-11-01). "Lattice Energy Calculations for (C6H5)5M0.5C6H12, M = P, As and Sb: Towards an Understanding
Pentaphenylphosphorus
Enthalpy change from diluting a substance in solution
molecular interaction: the breaking of attraction between solute molecules (lattice energy), the breaking of attraction between solvent molecules, and the forming
Heat_of_dilution
Technique for determining surface structures
controlled by the incident electron energy. From the knowledge of the reciprocal lattice models for the real space lattice can be constructed and the surface
Low-energy electron diffraction
Low-energy_electron_diffraction
(2016). "Nickel Hydride Complexes". Chemical Reviews. 116 (15): 8373–8426. doi:10.1021/acs.chemrev.6b00259. PMID 27437790. Solid solution Lattice energy
Nickel_hydride
Lowest possible energy of a quantum system or field
zero-point energy "dead as a doornail". Zero-point energy was also invoked by Peter Debye, who noted that zero-point energy of the atoms of a crystal lattice would
Zero-point_energy
Measure of solvency/solution
Solubility equilibrium Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart Miscibility
Hydration_number
Chemical compound
Holger Kalkhof: Crystal Engineering on Industrial Diaryl Pigments Using Lattice Energy Minimizations and X-ray Powder Diffraction. In: The Journal of Physical
Pigment_Yellow_13
Born, proposed the Born–Haber cycle as a method for evaluating the lattice energy of an ionic solid. Haber has also been described as the "father of chemical
History_of_chemistry
Electricity generation by nuclear fusion
two light atomic nuclei combine to form a heavier nucleus and release energy. Devices that use this process are known as fusion reactors. Research on
Fusion_power
Conceptual opposite of an electron
position where one could exist in an atom or atomic lattice. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by
Electron_hole
Regular infinite tree structure used in statistical mechanics
Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have the same number of neighbors. The Bethe lattice was
Bethe_lattice
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