What is crystallography? What is the importance of crystallography in geology world and mineralogy world?

 What is crystallography?

Answer: Crystallography is a branch of mineralogy that deals with the study of the arrangement and bonding of atoms in crystalline solids and the geometric structure of crystal lattice.

     Most minerals are crystalline while a few are amorphous (Non-crystalline).

Amorphous or Non-Crystalline: Amorphous are solids, which have no definite atomic structure and chemical composition.

 Crystal: crystals are solid bounded by smooth more or less plane surfaces arranged in regular pattern and form due to the operation of inter-atomic forces. They are formed by the solidification of minerals from the gaseous and liquid state under suitable conditions. Crystal has a definite atomic structure and definite chemical composition.

Morphology or parts of a crystal:

Face: Faces are nothing but the smooth surfaces through which a crystal is bounded. The crystal faces are produced during the process of crystal growth.

Edge: The line of intersection formed by two adjacent crystal faces in a crystal is called edge.

Solid angle: the point of intersection formed by three or more adjacent crystal faces in a crystal is called a solid angle.

Interfacial angle: The angle formed by the intersection of two imaginary normals which are drawn from two adjacent crystal faces in a crystal is known as an interfacial angle.

Crystal system:

  On the basis of a crystallographic axis, (These are the imaginary lines passing through the center of the crystal, but not lying in the same plane and they are used as axes of reference for denoting the position of faces) the crystals are divided into six major subdivisions, known as ‘crystal-system.

    On the basis of the number of crystallographic axes, relative length of the crystallographic axes, and the angular relationship existing between the crystallographic axes, The crystals are divided into six systems-

1)      Isometric system: In an Isometric system, there are three crystallographic axes that are equal in length and mutually perpendicular to each other. These crystallographic axes are termed a1, a2, and a3.

 

     Symmetry elements of isometric system are-

a)      9 planes of symmetry-

3 axial planes - 1 horizontal, 2 vertical

6 diagonal planes

b)      13 axes of symmetry-

3 axes of four-fold symmetry

4 axes of threefold symmetry

2 axes of six-fold symmetry

c)       One center of symmetry is present

 

2)      Tetragonal system: In a tetragonal system, there are three crystallographic axes, two of which are equal in length and the third vertical one is comparatively bigger in length. But they are mutually perpendicular to each other and they can be termed as a1, a2, and c.

    

Symmetry elements of the tetragonal system are-

a)      5 planes of symmetry

3 axial planes- 1 horizontal, 2 vertical

2 diagonal planes

b)      5 axes of symmetry-

1 axis of four folds symmetry

4 axes of two-fold symmetry

c)       One center of symmetry is present.

 

3)      Hexagonal system: In a hexagonal system, there are four crystallographic axes, three of which are equal in length and the fourth vertical one is comparatively bigger in length. Here three crystallographic axes are placed in such a way that all three axes make 90-degree angles with the vertical one.  These axes can be termed as a1, a2, a3 and c

    

 Symmetry elements of the hexagonal system are-

a)      7 planes of symmetry

4 axial plane- 1 horizontal, 3 vertical

3 diagonal planes

b)      7 axes of symmetry-

1 axis of six folds symmetry

6 axes of two folds symmetry

c)       One center of symmetry is present

 

4)      Monoclinic system: In a monoclinic system, there are three crystallographic axes that are not equal in length. They can be termed as a, b and c. Here two crystallographic axes are inclined to each other and the third vertical one is perpendicular.

 

5)      Triclinic system: In the triclinic system, there are three crystallographic axes that are not equal in length. They can be termed as a, b and c. Here all three crystallographic axes are inclined to each other.

 

6)      Orthorhombic system: In an orthorhombic system, there are three crystallographic axes that are not equal in length but mutually perpendicular to each other. They can be termed as a, b and c.

Crystal Forms: It is a group of faces, which have a like position with respect to the crystallographic axes of reference.

Forms may be classified into three types-

1)      Simple and combination forms: When a crystal is made up of all like faces such as cube, octahedral, etc. then the crystal is said to have a simple form.

     When a crystal is made up of two or more simple forms, then the crystal is said to have a combination form. For example- basal Pinacoid and prism face formed a combination form. Here both basal Pinacoid and prism are simple form crystals.

 

2)      Open and Close form: open forms whose faces cannot enclose space all by themselves, as they do not have an adequate number of faces to do so and as a result, occur only in combination with other forms

       The close form is an assemblage of faces, which can enclose a volume of space.

 

3)      General form, special form, and Restricted form:

      The general form is one in which the indices are unrestricted in magnitude.

       In special form, only one possible set of values exist for the indices (hkl), only one octahedron (III) is possible in the cubic.

       When the forms are neither special nor general, then the form of the crystal is called the restricted form.

Besides the above classification, Forms have also been classified as-

1)      Holohedral Forms: These forms exhibit the highest degree of symmetry possible in a system.

2)      Hemihedral Forms: These forms show half the number of faces required for the full symmetry of the system, for example-Tetrahedral is a Hemihedral form of Octahedron.

3)      Hemi-Morphic Forms: These forms have dissimilar faces about the two ends of an axis of symmetry. This axis is called the polar axis.

4)      Tetrahedral Forms: They show only a quarter of the number of faces of the corresponding Holohedral form. These forms have neither plane nor center of symmetry. 

5)      Enantiomorphic Forms: These forms do not have either plane or center of symmetry and occur in two positions, which are mirror images of each other.

Common Forms in Crystallography-

1)      Pedion: It is represented by one face only.

2)      Pinacoid: It is an open form, consisting of two faces that cut one crystallographic axis and remain parallel to the remaining axes.

3)      Prism: It is also an open form, consisting of four faces, each face of which essentially parallels the vertical axis and cuts one or more horizontal axes.

4)      Pyramid: It is a closed-form having eight faces, each face of which cuts the vertical axis and cuts one or more horizontal axes, at an equal or unequal distance.

5)      Domes: It is an open form intermediate between a prism and a pyramid, whose faces cut the vertical axis and one of the horizontal axes. These are also known as “Horizontal Prism”.

6)      Diametral Prism: It is formed by the combination of three Pinacoids which together enclose space. They occur only in the Orthorhombic, Monoclinic, and Triclinic systems in which all the Pinacoid occur.

 

Symmetry: Symmetry is a kind of regularity that can be expressed with respect to an axis, a plane, and the center of a crystal.

Axis of symmetry: Axis of symmetry or axis of rotation is an imaginary line passing through a crystal in such a way that when the crystal is rotated about this axis, it shows the same appearance more than once incomplete one rotation.

Plane of symmetry: A plane of symmetry is an imaginary plane passing through the center of a crystal in such a way that the plane divides the crystal into two equal portions, which are exactly the mirror image of each other.

Center of symmetry: Center of symmetry is an imaginary point in a crystal that any line drawn through this point intersects the crystal faces at equal distance.

On the basis of symmetry elements, the crystal systems are divided into classes-

In an isometric system, there are 7 classes –

1)      Cube

2)      Octahedron

3)      Dodecahedron

4)      Tetra hexahedron

5)      Trisoctahedron

6)      Trapezohedron

7)      Hex octahedron

In the tetragonal system, there are also 7 classes-

1)      Base

2)      First-order prism

3)      Second-order prism

4)      Di tetragonal prism

5)      First-order pyramid

6)      Second-order pyramid

7)      Di tetragonal pyramid

In hexagonal system, there are also 7 classes-

1)      Base

2)      First-order prism

3)      Second-order prism

4)      Di hexagonal prism

5)      First-order pyramid

6)      Second-order pyramid

7)      Di hexagonal pyramid

Laws of constancy of interfacial angles: Law of constancy of interfacial angle states that “the interfacial angles between corresponding faces are constant for all crystals of a given mineral”.

Axial ratio: The “unit length” of crystallographic axes is the length of the unit cell edges. The ratio which expresses the relative lengths of the unit cell edges along crystallographic axes is called the axial ratio. For example- in a sulfur crystal belonging to the orthorhombic system, the axial ratio is a: b: c = 0.8131: 1: 1.9034.