CLASSIFICATION OF CRYSTALS 3 (The Tetragonal system)

2)    The Tetragonal System

Figure 31: The crystallographic axes of the tetragonal system

 

-         The crystals in this system are referred to by 3 crystallographic axes which are perpendicular (90^o) to each other.

-         The two horizontal axes are equal in length and labeled a₁ a₂ while the third axis is either longer or shorter and labeled c.  That is a = b≠ c  (a₁ = a₂  ≠ c)

-         Its axial angles are such that α = β = γ = 90^o

-         The unit form is a system made up of straight prisms with square bases.

-         The diagnostic property if this system is a unique 1^iv axis on the c crystallographic axis.

The Tetragonal system has 7 classes as follows:

a)     The Tetragonal holosymmetric (Ditetragonal bipyramidal) class or the Zircon type.

b)    The Tetragonal hemimorphic (Tetragonal pyramidal) class

c)     The Tetragonal Sphenoidal Class

d)    The Tetragonal Bipyramidal class

e)     The Ditetragonal hemimorphic (Ditetragonal pyramidal) class

f)      The Tetragonal scalenohedral (tetragonal bisphenoidal) class

g)     The Tetragonal Trapezohedral class.

          The holohedral class of the system is the Tetragonal holosymmetric (Ditetragonal bipyramidal) class or zircon type with the following elements of symmetry:

-         A center of symmetry

-         5 planes of symmetry (3 axial and 2 diagonal)

-         5 axes of symmetry (1^iv and 4ⁱⁱ)

Forms in the Tetragonal System:

1.     Basal pinacoid: It is a form composed of 2 parallel faces perpendicular to the c crystallographic axis.  The basal pinacoids exist in combination with the various prisms of this system which include:

-         Tetragonal Prisms of the 1^st order {I I 0 } and

-         Tetragonal Prisms of the 2^nd order {0 I 0 }

NB: Prisms of the 1^st order are those whose faces intersect one horizontal axis and are parallel to the rest while Prisms of the 2^nd order are those whose faces intersect two horizontal axes and are parallel to the rest.

2.     Bipyramids {I I 0 }, which is a combination of prisms, bipyramids and pinacoids;

 Tetragonal bipyramids of 1^storder whose faces intersect all 3 crystallographic axes symbolized as {I I I }

          Tetragonal bipyramids of 2^nd order whose faces intersect the vertical crystallographic axis and 1 other horizontal crystallographic axis and is parallel to the other horizontal axis.

Examples of some minerals with this form include: Idocrase, zircon, Rutile and Cassiterite.  Of them all, Idocrase shows a combination of all the forms in the tetragonal system.