Isometric system: Definition:
All those crystals that can be referred to three crystallographic axes, which are essentially equal in length at right angles to each other, and mutually interchangeable, are said to belong to the isomeric or cubic system.

**Isometric,
Hexagonal and Monoclinic system**

**Isometric system: **

**Definition:**

All those crystals that can be
referred to three crystallographic axes, which are essentially equal in length
at right angles to each other, and mutually interchangeable, are said to belong
to the isomeric or cubic system.

**Axial diagram**

Since all the three axes are
equal and interchangeable these are represented by the letter a. In the study
position however the axes may be designated as a1,a2 and a3 the last being
vertical.

**Classes**

Five symmetry classes fall in the
Isometric system by virtue of their country The normal class is known as galena
type. It has got the following symmetry.

a) **Axes
of symmetry:**

13 in
all

3 are
axes of four-fold symmetry

4 are axes
of three-fold symmetry

6 are axes
two fold of symmetry

b) **Planes of
Symmetry**: 9 in all** **

3 planes of
symmetry are at right angles to each other and are termed the principal planes;

6 planes
f symmetry are diagonal in position and bisect the angles between the principal

planes.

c) **It has centre of symmetry.**

**Forms**

Following are the forms that
commonly develop in the crystals belonging to isometric system.

1. Cube: A
form bounded by six similar square faces each of which is parallel to two of
three crystallographic axes and meets the third axis.

2. Octahedron:
A form bounded by eight similar faces each of the shape of an equilateral
triangle each meeting the three crystallographic axes at equal distances.

3. Dodecahdraon:
It is form with twelves similar faces each of which is parallel to one of the
three crystallographic axes and meets the other two at equal distances.

4. Trisoctahedron:
A form of twenty four faces; each face meeting two axes at unit length and to
the third at greater that unity.

5.Trapezohedran: A forms of 24
faces each faces meeting one axes at unit length and to the other two at
greater than unity.

6. Hexaoctahedran:
48 faces; each face meets the three axis at unequal distances.

7. Tetra
hexahedron: 24 faces each face meeting one axes and meet other to at unequal
distance which are simple multiple of each other.

**Other
classes:**

Isometric
system comprises five symmetry classes in all. Beside the normal class
following three classes are also represented among the minerals.

**1.Pyritohedral
Class**

a) Symmetry : 7 axes of symmetry of which 3 are axial axes of two
fold symmetry 4 are diagonal axes of two fold symmetry,3 planes of symmetry. A
centre of symmetry.

b) Forms : Pyritohedran and Diploid
are two typical forms of this symmetry class. Diploid is a closed form of
twenty-four faces that typically occur in pairs.

**2.Tetrahedral
class**

a) Symmetry :
7 axes of symmetry, 6 planes of symmetry diagonal, no centre of symmetry.

b) Forms : Most typical form of this class is a
four-sided solid in which each face is an equilateral triangle. It is termed
tetrahedron. It has a general symbol.

**Hexagonal
system**

All those
crystals, which can be referred to four crystallographic axes of which

i.Three
axes are horizontal, equal, interchangeable and intersecting each other at 120^{0}
between the positive ends.

ii.The
fourth axes are vertical and at right angles to the three horizontal axes are
grouped under the hexagonal system.

**Axial
diagram**

The horizontal axes all being equal are designated
by the letter a(a1,a2,a3)and the vertical axis by the letter 'c' as
usual.

**Forms**

Forms of hexagonal system differ
in character from forms of all the other systems in that their parameters,
indices and symbols are determined with respect to four crystallographic axes.
Thus the general form expresses the relation of any hexagonal form.

1. Base: An
open form of two faces in which each face meets the vertical axis only.

2. Prisms: A
prism as defined earlier is an open form in which each face is essentially
parallel to the vertical axis.

Following three types of prisms are met with in the hexagonal
system.

a) Prism of
1^{st} order. An open form of six faces in which each face is parallel
to one of the three horizontal axes besides the vertical axis. It cuts the two
horizontal axes at unit length.

b) Prism of
2^{nd} order. An open form of six faces like prism of 1^{st}
order but in this case each face cuts all the three horizontal axes, two axes
at equal length and to the third at greater length.

c) Prism of
3^{rd} order: It is also called a dihexagonal prism as it has double
the number of faces compared to the six faces of prism of 1^{st} order.

**Monoclinic system**

The monoclinic system includes
all those forms that can be referred to three crystallographic axes which are
essentially unequal in length and further that can be of these is always
inclined.

**Axial diagram**

All the three axes are unequal,
they are designated by the letters a, b and c. The c axis is always vertical.
The inclined axis is a- axis. It is inclined towards the observer and is also
referred as clino axis.

**Normal class symmetry**

There are
three symmetry classes placed in monoclinic system. The symmetry of the normal
class is as given below:

a) Axis of Symmetry : 1 axis of two
fold symmetry only

b) Planes of symmetry : 1 plane of
symmetry only. And a centre of symmetry. The plane of symmetry is that plane
which contains the crystallographic axes a and c.

**Forms**

The
common forms of this system are

**1)
Pinacoid**

it is an open from of two faces, each face being
parallel to the two axes and cutting the third at a unit length .Three
pinacoids are distinguished in the monoclinic system.

**2. Domes**

A dome is also form of two faces, each face
meeting the vertical axis and one of the other two axes. It is a parallel to
the third axis. Two types of domes are recognized:

i)

Orthodome

ii) Clinodome

**3. Prisms**

There are
three types of prisms is there;

i) Unit prism

ii) Orthoprism

iii) Clinoprism

**4.
Pyramid**

These are closed forms and in these each face
meets all the three axes.

i)
Unit pyramid

ii)
Orthopyrmaid

iii)
Clinopyramid

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Civil : Engineering Geology : Mineralogy : Isometric, Hexagonal and Monoclinic system |

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