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Crystallization is a process that leads to solids with highly organized atoms or molecules, i.e. a crystal. The ordered nature of a crystalline solid can be contrasted with amorphous solids in which atoms or molecules lack regular organization.
Crystallization of polymers is a process associated with partial alignment of their molecular chains. These chains fold together and form ordered regions called lamellae , which compose larger spheroidal structures named spherulites .
The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement. (Quasicrystals are an exception, see below). Not all solids are crystals.
Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established. [5] [6] The discovery of X-rays and electrons in the last decade of the 19th century enabled the determination of crystal structures on the atomic scale, which brought about the modern era of crystallography.
By definition, the syntax (hkℓ) denotes a plane that intercepts the three points a 1 /h, a 2 /k, and a 3 /ℓ, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell (in the basis of the lattice vectors).
He provided a clear definition of surface energy, by which the concept of surface tension is made applicable to solids as well as liquids. He also appreciated that an anisotropic surface free energy implied a non-spherical equilibrium shape , which should be thermodynamically defined as the shape which minimizes the total surface free energy .
For the crystallization of hard spheres the classical theory is a very reasonable approximate theory. [9] So for the simple models we can study, classical nucleation theory works quite well, but we do not know if it works equally well for (say) complex molecules crystallising out of solution.
In Schoenflies notation, point groups are denoted by a letter symbol with a subscript. The symbols used in crystallography mean the following: C n (for cyclic) indicates that the group has an n-fold rotation axis. C nh is C n with the addition of a mirror (reflection) plane perpendicular to the axis of rotation.