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. [1]
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
which amounts to −786 kJ/mol. [2]
Some chemistry textbooks [3] as well as the widely used CRC Handbook of Chemistry and Physics [4] define lattice energy with the opposite sign, i.e. as the energy required to convert the crystal into infinitely separated gaseous ions in vacuum, an endothermic process. Following this convention, the lattice energy of NaCl would be +786 kJ/mol. Both sign conventions are widely used.
The relationship between the lattice energy and the lattice enthalpy at pressure is given by the following equation:
where is the lattice energy (i.e., the molar internal energy change), is the lattice enthalpy, and the change of molar volume due to the formation of the lattice. Since the molar volume of the solid is much smaller than that of the gases, . The formation of a crystal lattice from ions in vacuum must lower the internal energy due to the net attractive forces involved, and so . The term is positive but is relatively small at low pressures, and so the value of the lattice enthalpy is also negative (and exothermic).
The lattice energy of an ionic compound depends strongly upon the charges of the ions that comprise the solid, which must attract or repel one another via Coulomb's Law. More subtly, the relative and absolute sizes of the ions influence . London dispersion forces also exist between ions and contribute to the lattice energy via polarization effects. For ionic compounds made of molecular cations and/or anions, there may also be ion-dipole and dipole-dipole interactions if either molecule has a molecular dipole moment. The theoretical treatments described below are focused on compounds made of atomic cations and anions, and neglect contributions to the internal energy of the lattice from thermalized lattice vibrations.
In 1918 [5] Born and Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term. [2]
where
The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors:
Barium oxide (BaO), for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of −3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of −786 kJ/mol. The bond radii are similar but the charge numbers are not, with BaO having charge numbers of (+2,−2) and NaCl having (+1,−1); the Born–Landé equation predicts that the difference in charge numbers is the principal reason for the large difference in lattice energies.
Closely related to this widely used formula is the Kapustinskii equation, which can be used as a simpler way of estimating lattice energies where high precision is not required. [2]
For certain ionic compounds, the calculation of the lattice energy requires the explicit inclusion of polarization effects. [7] In these cases the polarization energy Epol associated with ions on polar lattice sites may be included in the Born–Haber cycle. As an example, one may consider the case of iron-pyrite FeS2. It has been shown that neglect of polarization led to a 15% difference between theory and experiment in the case of FeS2, whereas including it reduced the error to 2%. [8]
The following table presents a list of lattice energies for some common compounds as well as their structure type.
Compound | Experimental Lattice Energy [1] | Structure type | Comment |
---|---|---|---|
LiF | −1030 kJ/mol | NaCl | difference vs. sodium chloride due to greater charge/radius for both cation and anion |
NaCl | −786 kJ/mol | NaCl | reference compound for NaCl lattice |
NaBr | −747 kJ/mol | NaCl | weaker lattice vs. NaCl |
NaI | −704 kJ/mol | NaCl | weaker lattice vs. NaBr, soluble in acetone |
CsCl | −657 kJ/mol | CsCl | reference compound for CsCl lattice |
CsBr | −632 kJ/mol | CsCl | trend vs CsCl like NaCl vs. NaBr |
CsI | −600 kJ/mol | CsCl | trend vs CsCl like NaCl vs. NaI |
MgO | −3795 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. MgO is insoluble in all solvents |
CaO | −3414 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. CaO is insoluble in all solvents |
SrO | −3217 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. SrO is insoluble in all solvents |
MgF2 | −2922 kJ/mol | rutile | contrast with Mg2+O2- |
TiO2 | −12150 kJ/mol | rutile | TiO2 (rutile) and some other M4+(O2-)2 compounds are refractory materials |
In thermodynamics, enthalpy, is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant external pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work that was done against constant external pressure to establish the system's physical dimensions from to some final volume , i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation, and other chemical "energies" are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.
Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be more complex, e.g. molecular ions like NH+
4 or SO2−
4. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal to obtain a full valence shell for both atoms.
An intermolecular force (IMF) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics.
In chemistry, a salt or ionic compound is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a neutral compound with no net electric charge. The constituent ions are held together by electrostatic forces termed ionic bonds.
In electromagnetism, a dielectric is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarised, but also reorient so that their symmetry axes align to the field.
Solvation describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the solute, including solubility, reactivity, and color, as well as influencing the properties of the solvent such as its viscosity and density. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. The surrounded solute particles then move away from the solid solute and out into the solution. Ions are surrounded by a concentric shell of solvent. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes and involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a solute by water is called hydration.
Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Joseph Valasek. Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric and ferromagnetic are known as multiferroics.
In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The standard pressure value p⦵ = 105 Pa(= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is ΔfH⦵. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K).
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities of the chemical species undergoing reduction and oxidation respectively. It was named after Walther Nernst, a German physical chemist who formulated the equation.
The Born–Haber cycle is an approach to analyze reaction energies. It was named after two German scientists, Max Born and Fritz Haber, who developed it in 1919. It was also independently formulated by Kasimir Fajans and published concurrently in the same journal. The cycle is concerned with the formation of an ionic compound from the reaction of a metal with a halogen or other non-metallic element such as oxygen.
In chemistry, bond energy (BE), also called the mean bondenthalpy or average bond enthalpy is a measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy for all bonds of the same type within the same chemical species.
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.
Ionic radius, rion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 31 pm (0.3 Å) to over 200 pm (2 Å).
In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m−3), at any point in a volume. Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m−1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative.
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.
This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.
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.
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.