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.