Lattice energy is the energy per ion pair required to separate completely the ions in a crystal lattice at a temperature of absolute zero.
Hexagonal crystal system is based on four crystallographic axes. The system of crystallographic axes of the hexagonal crystal system consists of three equivalent horizontal (equatorial) axes of which the positive ends make an angle of 120°. These axes are sometimes denoted as a, b and d axes. The fourth axis is (c) is perpendicular to and shorter or longer than the other three.
Polymorphism is the ability of a solid substance to crystallise into more than one different crystal structure. Different polymorphs have different arrangements of atoms within the unit cell, and this can have a profound effect on the properties of the final crystallised compound. The change that takes place between crystal structures of the same chemical compound is called polymorphic transformation.
The set of unique crystal structures a given compound may form are called polymorphs. Calcium carbonate is dimorphous (two forms), crystallizing as calcite or aragonite. Titanium dioxide is trimorphous; its three forms are brookite, anatase, and rutile. The prevailing crystal structure depends on both the temperature and the external pressure.
Iron is a metal with polymorphism structure. Each structure stable in the range of temperature, for example, when iron crystallizes at 1 538 °C it is bcc (δ-iron), at 1 394 °C the structure changes to fcc (γ-iron or austenite), and at 912 °C it again becomes bcc (α-iron or ferrite).
Polymorphism of an element is called allotropy.
Allotropes are the elements which exist in two or more different forms in the same physical state. Allotropes generally differ in physical properties and may also differ in chemical activity.
Diamond, graphite and fullerenes are three allotropes of the element carbon. Graphite is a soft, black, slippery substance; by contrast, diamond is one of the hardest substances known. The different properties of the allotropes arise from their chemical structures. Diamonds typically crystallize in the cubic crystal system and consist of tetrahedrally bonded carbon atoms. Graphite crystallizes in the hexagonal system. In the fullerenes, the carbon atoms taking the form of a hollow sphere, ellipsoid, or tube.
In some cases, the allotropes are stable over a temperature range, with a definite transition point at which one changes into the other. For instance, tin has two allotropes: white (metallic) tin stable above 13.2 °C and grey (nonmetallic) tin stable below 13.2 °C.
The term allotropes may also be used to refer to the molecular forms of an element. Ozone is a chemically active triatomic allotrope of the element oxygen.
Born-Haber cycle is a cycle of reactions used for calculating the lattice energies of ionic crystalline solids. For a compound MX, the lattice energy is the enthalpy of the reaction
The standard enthalpy of formation of the ionic solid is the enthalpy of the reaction
The cycle involves equating this enthalpy (which can be measured) to the sum of the enthalpies of a number of steps proceeding from the elements to the ionic solid. The steps are:
1) Atomization of the metal
2) Atomization of the nonmetal
3) Ionisation of the metal
This is obtained from the ionisation potential.
4) Ionisation of the nonmetal
This is electron affinity.
5) Formation of the ionic solids
Equation of the enthalpies gives
from which ΔHL can be found.
Generalic, Eni. "Heksagonska rešetka." Croatian-English Chemistry Dictionary & Glossary. 29 June 2022. KTF-Split. {Date of access}. <https://glossary.periodni.com>.
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