Crystalline form

A crystalline form is a whole of faces of a Cristal which are in a report/ratio of Symétrie.

A crystalline form is characterized by:

* the multiplicity which is the number of the faces; it depends on the symmetry of the crystal and the orientation on the original face compared to the elements of symmetry of the crystal

* its own symmetry

* its official name. The French official nomenclature of the crystalline forms was published in: J.D.H. Donnay and H. Curien, “Nomenclature of the 47 crystalline forms” Bulletin of the French company of Mineralogy and Crystallography , 81 (1958) XLIV-XLVII.

Representation of the crystalline forms

One distinguishes two kinds of crystalline form:

the open forms whose faces do not form rigorously a Volume; one or more faces of the Volume not belonging to the crystalline form. In the charts, one recognizes these forms with the absence of one or more faces; absence which can be appeared for example using polygons chopped like below.
the closed forms which are volumes, no face not missing.

A crystal cannot thus consist of only one opened form, while it can develop only one closed form.

A form is indicated by the indices of one of its faces, preferably that which has the most positive values. The indices of a form are written between accodances.

Example

The form {111} includes/understands the face (111) and all the faces equivalent to (111) by symmetry.

If the specific group of the crystal is $\ bar {1}$ , the form {111} has multiplicity 2 and is made up of two parallel plans, $(111)$ and $(\ bar {1} \ bar {1} \ bar {1})$ : this form is called pinacoidal .
If the specific group of the crystal is $m \ bar {3} m$ , the form {111} has multiplicity 8 and is made up of eight faces which are triangles équilatères: $(111)$ , $(11 \ bar {1})$ , $(1 \ bar {1} 1)$ $(\ bar {1} 11)$ , $(1 \ bar {1} \ bar {1})$ , $(\ bar {1} 1 \ bar {1})$ , $(\ bar {1} \ bar {1} 1)$ and $(\ bar {1} \ bar {1} \ bar {1})$ . This form is a Octaèdre .

Classification of the crystalline forms

Among the various criteria of classification, the following is most important:

I - characteristic Forms and not-characteristics

This criterion integrates the possibility of crystals of different symmetries of developing the same form.

Let us note G the specific group which correspond to the clean symmetry of the form and H the specific group of the crystal which developed this form: either H coincides with G itself; maybe with one of its sub-groups, which one writes H $\ subseteq$ G .

When H = G , one speaks about forme caractéristique, while H $\ subseteq$ G corresponds to a forme non-caractéristique. In the crystalline systems triclinic and monoclinical, any form is not-characteristic.

II - general and particular Forms

When the poles of the faces of a crystalline form are on elements of symétre (axes or mirrors), the form is known as particulière, if not it is générale.

Example 1

The prism ditétragonal with clean symmetry 4 mm : it is presented like forms { HK 0} in the specific groups 4 mm , $\ bar {4} 2m$ , 4 mm and 422. It is thus only in the first case that it is about a characteristic form .

Example 2

The prism tétragonal is presented like forms {100} in all the tétragonaux specific groups. However, it is about a particular form in groups 4 mm , $\ bar {4} 2m$ , 4 mm , 422 and 4 m , but of a general form in the groups $\ bar {4}$ and 4.

III - basic Forms and limits

When a form can be obtained like limit of another form having the same multiplicity (many faces) and the same orientation but a higher clean symmetry, this form is called forme limite and that from which this form was obtained calls forme basique.

Example

In the specific group 4 mm the pyramid tétragonale and the prism tétragonal have multiplicity 4 and can be directed either according to the axes or according to the bisectrices of the axes. The pyramid, forms basic, has clean symmetry 4 mm while the prism, forms limit, has clean symmetry 4 mm . The prism can be imagined like the result of the opening of the pyramid at its top and the break of the slope of the faces, until the limit where those become parallel, thus forming a prism.

47 crystalline forms

The open forms are shown below with polygons chopped to indicate the not closed plans.

Pedion

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