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The hpc lattice (left) and the ccf lattice (right) The principles involved can be understood by considering the most efficient way of packing together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For example, if plane A lies beneath plane B, there are two possible ways of placing an additional atom on top of ...
simple cubic lattice. The atoms in the unit cell are at the corner of a cube. γ-O (none) Cubic: Pm 3 n (No. 223) 16: Closely related to the β-W structure, except with a diatomic oxygen molecule in place of each tungsten atom. The molecules can rotate in place, but the direction of rotation for some of the molecules is restricted.
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...
Mesomorphic states: States of matter intermediate between solid and liquid. Plastic crystal: A molecular solid with long-range positional order but with constituent molecules retaining rotational freedom. Liquid crystal: Properties intermediate between liquids and crystals. Generally, able to flow like a liquid but exhibiting long-range ...
A simple cubic crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths a, b, and c of the three cell edges meeting at a vertex, and the angles α, β, and γ between those edges. The crystal lattice parameters a, b, and c have the
Forms of matter that are not composed of molecules and are organized by different forces can also be considered different states of matter. Superfluids (like Fermionic condensate) and the quark–gluon plasma are examples. In a chemical equation, the state of matter of the chemicals may be shown as (s) for solid, (l) for liquid, and (g) for gas.
A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...
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.