In mineralogy and crystallography, a crystal (from the greek κρύσταλλος, krýstallos, ice) is defined as the atomic or molecular structure that matter in the solid state presents, chemically and physically homogeneous. In other words atoms, molecules or ions have a regular three-dimensional geometric arrangement, which is repeated indefinitely in the three spatial dimensions, called crystal lattice or Bravais lattice.
The regular arrangement of the three-dimensional structure is characteristic of the type of material and produces the characteristic shape of crystals (morphology) defined by characteristic faces and dihedral angles; consequently, the relative properties of crystalline substances also depend on their particular intimate structure and not on the polyhedral shape they assume. Crystalline solids exhibit planes of flaking that are related to the shape of the crystal building.
The same substance sometimes has more than one crystalline form, depending on the temperature and pressure at which it solidifies. This property is called polymorphism when referred to a compound (e.g. calcite, aragonite) and allotropy when referred to an element (e.g. diamond, graphite, fullerenes).
There are many cases in which different substances, but able to give crystals with the same structure, even at the molecular level, show a mutual and complete miscibility in the state (mixed crystals). This property is called isomorphism.
Typical characteristic of crystalline solids is the anisotropy: property of a substance for which the values of its physical quantities (refractive index, electrical and thermal conductivity, hardness, etc.) depend on the direction that is considered.
There are materials that have a lower degree of crystallinity, such as certain polymers, which have only a two-dimensional order, and many synthetic or natural fibers, which are ordered only along the axis of the fiber.
Some organic crystals, when properly heated, go to an intermediate state between solid and liquid, which is called the mesomorphic or liquid crystal state. Materials with this behavior also include coordination compounds.
Most minerals are polycrystalline, that is, they are composed of many crystals (crystallites), although this is not usually visible to the naked eye, because the individual crystals are microscopic in size. In contrast, solids consisting of a single crystal (called monocrystals) are very rare. Non-crystalline solids (such as glass) are called amorphous.
A crystal is a solid formation that has a periodic and ordered arrangement of atoms at the vertices of a lattice structure, the crystal lattice; the presence of such atomic organization can give the crystal a definite geometric shape. Crystals are formed by the gradual solidification of a liquid or by the frosting of a gas. Such crystallization can occur spontaneously in nature or be artificially reproduced.
The type of structure assumed by the crystal plays a determining role in many of its properties, such as flaking. Depending on the symmetries of their structure, many properties, such as electrical, optical and mechanical (e.g. Young’s and Poisson’s moduli), can be anisotropic, i.e. dependent on their orientation in space. In contrast, only some crystals are isotropic.
The formation and characteristics of a crystal depend on the rate and conditions of solidification (also called “crystallization”). For example, the liquids that form granite are erupted to the surface as volcanic lava and cool relatively slowly. If cooling is more rapid, an aphanitic rock is formed, with crystals not visible to the naked eye; even slower cooling leads to the formation of large crystals.
Crystalline habit is defined as the typical appearance of crystals determined by the relative development of the faces and the prevalence of one or more characteristic simple geometric shapes. The main conditions that can influence growth are:
- duration of accretion;
- chemical composition;
- space available for growth.
Crystals have a discontinuous and periodic three-dimensional structure, they are formed by particles (leptons) arranged at regular intervals in the three dimensions of space, so that around each of these particles there is an equal distribution of material points.
Consequence of the structure of crystals is the anisotropy of the same, that is the fact that in them vary from point to point the properties characterized by the direction (vector properties, such as electrical conductivity, cohesion, thermal expansion), while remain unchanged the properties independent of the direction (scalar properties, such as specific gravity and fusibility). In this differ the amorphous substances, which present equality at every point of both scalar and vector properties and are therefore called isotropic.
The macroscopic shape assumed by crystals is a consequence of their intimate structure, but not always the crystal has a well-defined macroscopic shape: in fact during crystallization can intervene factors (such as the proximity of crystals being formed) that hinder the regular growth of the crystals themselves and can lead, for example, to the formation of individuals without a well-defined shape. In nature, in fact, crystals almost never develop in isolation, but next to each other in more or less ordered associations (aggregates) or in associations regulated by precise laws (geminates).
Even if it is the intimate structure to define crystals, their shape is very important: its study has allowed the formulation of three fundamental laws: the law of dihedral angle constancy, the law of rationality of indices and the law of symmetry constancy.
The first law, initially studied in 1665 by N. Stenone, then validated in the late eighteenth century by J. B. Romé de l’Isle, concerns the external shape of crystals and establishes that in crystals of the same substance, as long as the temperature does not vary, the dihedral angles of two corresponding faces are always equal, whatever the development and the shape of the faces themselves. It follows that to define the geometric form of a crystal it is possible to disregard its real form and refer exclusively to the mutual position of the faces defined by the meeting of them; and since the angles that they form do not vary whatever the development of the faces, it will always be possible to bring a disproportionate crystal to a model crystal, giving to each face the same development.
The second law, or Haüy’s law, concerns the position of the different faces in a crystal and the relationship of these with another, taken as a reference and called “fundamental face”; it says that “if we assume as coordinate axes three real or possible edges of the crystal, the relationships between the parameters cut on the same axes by two faces of the crystal are rational and simple numbers”.
To know the position of the faces we place the crystal so that its fundamental face meets the coordinates (crystallographic axes) in three points: the distance between the origin of the coordinates and the meeting points takes the name of parameter for each coordinate, so three parameters for each face. To study a face we must know its parameters and compare them with those of the fundamental face: the ratios that result from this comparison are called “indices”.
The law of rationality of indices takes into account these values and establishes that they are always expressed by generally small integers. The crystallographic axes are designated with x, y, z; their origin, imagined inside the crystal, with O; the angles between the axes are α between y and z, β between z and x, γ between x and y; the ratios between the parameters of a face with the parameters of the fundamental one, that is the indices, with h, k, l.
The third law (law of constancy of symmetry) regulates the number of faces and the particular shape to be given to the crystals of each mineral species. When we study a crystal we resort to its symmetry and, precisely, this is established according to certain elements called planes of symmetry, axes of symmetry and center of symmetry.
The plane of symmetry (p) of a crystal is that plane which divides it into two equal parts such that one is the mirror image of the other. Axis of symmetry of a crystal is the straight line around which the crystal rotates an angle equal to 360º/n (n indicates an integer other than 1) to recapture the initial position.
The axes of symmetry can be binary, ternary, quaternary and senary, n will be equal to 2, 3, 4 or 6 and are indicated with A2, A3, A4 and A6; the letter p is added to the index if the axes are polar, that is if at their ends the crystal has different physical properties.
The center of symmetry (c) is that point from which depart physically equal directions and counterdirections, so that every face corresponds to another parallel and inverted, and every edge and every vertex corresponds to an analogous element. In every crystal the center is always unique, while the other elements of symmetry can be even greater in number, there are crystals that have many elements of symmetry and crystals that have few, the set of symmetry elements is the degree of symmetry and serves for the classification of various minerals that occur in the crystalline state.