‫بسم هللا الرحمن الرحيم‬
‫وفي االرض آيات للموقنين‬
‫أفال تبصرون‬
‫من سورة الذاريات اية ‪ 20‬و‪21‬‬
MOSUL - UNIVERSITY
PETROLEUM AND
MINING
ENGINEERING COLLEGE
PETROLEUM RESERVOIR
DEPARTMENT
Dr. MOHMMED SALEEM Y.
AL-BAKKAL
Crystal Axes, Systems, Mineral Face
Notation (Miller Indices)
USC Mineralogy Geol 315 (Anderson)
A CRYSTAL is the outward form of the
internal structure of the mineral.
The 6 basic crystal systems are:
ISOMETRIC
TETRAGONAL
Drusy Quartz on Barite
MONOCLINIC
Acknowledgement: the following images from Susan
and Stan Celestian, Glendale Community College
HEXAGONAL
ORTHORHOMBIC
TRICLINIC
Crystallography
Crystallography: the study of these solid bodies and
laws that govern their , external shape, and internal
atomic structures using x-ray and x-ray diffraction.
Crystals: A homogeneous solid body possessing
long-range three dimensional internal order
bounded by natural plane faces that are external
expression of a regular internal arrangement of
constituent atoms , molecules or ions .
Crystals and degree of crystallinity
Euhedral : A crystalline solid with well-formed faces
Subhedral : If it has imperfectly developed faces.
Anhedral : If it is with-out faces
Avery fine crystals can be determined only with aid
of microscope designated as Microcrystalline.
Crystalline aggregated so finely divided that the
crystals cannot be resolved with the microscope yet
pattern give a diffraction pattern with x-ray are
cryptocrystalline.
A few solids lack any ordered internal structure
These said to be Amorphous.
crystal parts are divided in to two groups:
first Real Parts.
1- Crystal Faces : The Plane surface that are the more
obvious feature of crystals are parallel to net planes in
crystal-structure, faces are two kinds, like and unlike.
Crystals with like faces termed a simple form.
A Crystals which are consist of two or more simple
forms is called a combination.
2- Edge: Line is formed by intersection of any two adjacent
faces.
3- Solid Angle :Angle is formed by intersection of Three
or more faces.
4- Interfacial Angle : The angle between two faces of
crystal as in fig.
Crystal Real Parts
Second Imaginary Parts
1- Crystallographic axes: Imaginary lines passing through
the crystal parallel to intersection of major crystal faces. All
the crystals, are referred to three crystallographic axes
designated as a , b and c, except of those belonging to
hexagonal system is referred to four crystallographic axes.
Crystals with three crystallographic axes:
The (a) axis is horizontal and in a front-back position.
The (b) axis is horizontal and right left position.
The (c) axis is vertical.
The ends of each axis are +or The front end of(a) the
right-hand end of (b) ; the
upper end of (c) are positive;
the opposite ends are negative
2-Interaxial angles: they are three angles( α , β & γ) at the center
of crystals in between crystallographic axes.
(α) Is between the axes (b & c)
(β )between the axes (a &c )
(γ) Is between the axes (a & b)
Crystals with four crystallographic axes
Hexagonal System referred to four crystallographic axes , three equal
horizontal axis (a1 ,a2 ,a3) intersect at angles of 120°, the fourth is (c)
of different length and perpendicular to plane of the other three .
a² axis is horizontal and right left position (position of b) .
a1+ axis is 120°in horizontal clock wise direction from a² +
a³+ axis position 120 in horizontal
clock wise direction from a1+.
α the angle is between c & a2+
β the angle is between a1+ & c+
γ the angle is between a²+ & a1+
Crystal Systems
Crystal Systems
CRYSTAL SYSTEMS are divided into 6 main groups
The first group is the ISOMETRIC
This literally means “equal
measure” and refers to the equal
size of the crystal axes.
ISOMETRIC - Fluorite Crystals
Crystal Systems
ISOMETRIC CRYSTALS
ISOMETRIC
In this crystal system there are 3
axes. Each has the same length (as
indicated by the same letter “a”).
a3
a2
a1
ISOMETRIC
Basic Cube
They all meet at mutual 90o angles
in the center of the crystal.
Crystals in this system are typically
blocky or ball-like.
ALL ISOMETRIC CRYSTALS HAVE
4 3-FOLD AXES

ISOMETRIC BASIC CRYSTAL SHAPES
Crystal Systems
Fluorite
Cube
Garnet
Trapezohedron
Pyrite
Cube with
Pyritohedron
Striations
Crystal Systems

ISOMETRIC CRYSTALS
a3
a3
a2
a1
a2
a1
ISOMETRIC - Basic Cube
Fluorite cube with
crystal axes.
Crystal Systems
HEXAGONAL CRYSTALS
c
a3
a1
a2
HEXAGONAL - Three
horizontal axes meeting at angles of
120o and one perpendicular axis.
HEXAGONAL Crystal
Axes
ALL HEXAGONAL CRYSTALS
HAVE A SINGLE 3- OR 6-FOLD
AXIS = C
Crystal Systems
HEXAGONAL CRYSTALS
These hexagonal
CALCITE crystals
nicely show the six
sided prisms as well as
the basal pinacoid.
Two subsystems':
1. Hexagonal
2. Trigonal
Crystal Systems
TETRAGONAL CRYSTALS
TETRAGONAL
Two equal, horizontal, mutually
perpendicular axes (a1, a2)
Vertical axis (c) is perpendicular to the
horizontal axes and is of a different
length
c
c
a1
a2
a2
a1
TETRAGONAL Crystal
Axes
This is an Alternative
Crystal Axes
The C-axis is always 4, 4bar, or 4/m
Crystal Systems

WULFENITE
TETRAGONAL CRYSTALS
Same
Same crystal
crystal seen
seen edge
edge on.
on.
ALL TETRAGONAL CRYSTALS HAVE A SINGLE 4-FOLD AXIS = C
Crystal Systems
ORTHORHOMBIC CRYSTALS

ORTHORHOMBIC
Three mutually perpendicular axes of different lengths.
c
c
b
a
ORTHORHMOBIC
Crystal Axes
b
a
An Alternative Crystal
Axes Orientation
Each axis has symmetry,
either 2-fold or m-normal
Crystal Systems

ORTHORHOMBIC CRYSTALS
Topaz from Topaz Mountain,
Utah.
Crystal Systems

ORTHORHOMBIC CRYSTALS
BARITE is also orthorhombic.
The view above is looking down
the “c” axis of the crystal.
Crystal Systems

ORTHORHOMBIC CRYSTALS
Pinacoid View
Prism View
STAUROLITE
Crystal Systems

MONOCLINIC CRYSTALS
MONOCLINIC
In this crystal form the axes are of
unequal length.
c
Axes a and b are perpendicular.
b
a
MONOCLINIC Crystal
Axes
Axes b and c are perpendicular.
But a and c make some oblique
angle and with each other.
MONO = ONE AXIS OF
SYMMETRY (2-FOLD OR
MIRROR) = TO “b”
Crystal Systems

MONOCLINIC CRYSTALS
Mica
Gypsum
Orthoclase
Crystal Systems

TRICLINIC CRYSTALS
c
TRICLINIC
a
b
TRICLINIC Crystal
Axes
In this system, all of the axes
are of different lengths and
none are perpendicular to any
of the others.
SYMMETRY: ONLY 1 OR 1-BAR
Crystal Systems

TRICLINIC CRYSTALS
Microcline, variety Amazonite
3-D Miller Indices (an unusually complex example)
a
b
c
unknown face (XYZ)
reference face (ABC)
2
1
2
4
2
3
invert
1
2
4
2
3
2
(1
4
3)
c
C
Z
clear of fractions
A
X
O
Miller index of
face XYZ using
ABC as the
reference face
Y
B
a
b
Example: the (110) surface
Example: the (111) surface
Example: (100), (010), and (001)
(001)
(010)
For the isometric system, these faces are equivalent (=zone)
Crystal Symmetry
Crystal Symmetry : Is regularity of arrangement of similar
faces and angles, and by preforming certain operations on
them the like faces and angles can be brought into coincidence
There four types of Symmetry :1-Symmetry Plane :Is an imaginary plane that divides a
crystal in two halves . each of which, in a perfectly
developed crystal , is the mirror image of the other.
2-Symmetry Axis of Rotation : Is an imaginary line through the crystal
about which the crystal may rotated and repeat itself in appearance
two or more times during a complete rotation.
3-symmetry center : If a crystal have center of symmetry , imaginary
line can be pass from any point on its surface through its center
and similar point at an equal distance is found beyond the center .
4-Symmetry Axis of Inversion : This composite symmetry element
combines a rotation about the axis with inversion through center .