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An Introduction to Crystallography
CONTENTSCrystallography:
 Why we study Crystallography?
 Definition
 External characteristics of crystals
• Elements of...
 Atomic structure
 Central region called the nucleus
 Consists of protons (+ charges) and neutrons
(- charges)
 Electr...
 Chemical bonding
 Formation of a compound by combining
two or more elements
 Ionic bonding
 Atoms gain or lose outerm...
 Covalent bonding
 Atoms share electrons to achieve
electrical neutrality
 Generally stronger than ionic bonds
 Both i...
Covalent bond Model
- diamond (Carbon)
 Polymorphs
 Minerals with the same composition but
different crystalline structures
 Examples include diamond and grap...
 Crystal form
 External expression of a mineral’s
internal structure
 Often interrupted due to competition for
space an...
Why we study Crystallography?
It is useful for the identification of minerals. The
later are chemical substances formed un...
Study of crystals can provide new chemical
information. In laboratories and industry, we can
prepare pure chemical substan...
DEFINITION
• CRYSTALLOGRAPHY is simply a fancy
word meaning "the study of crystals"
• The study of crystalline solids and ...
Classification of substances
• Crystalline Substances
• Amorphous substances
Properties of Crystalline Substances
1- Solidity 2- Anisotropy X Isotropy
3- Self-faceting ability 4- Symmetry
space latti...
Amorphous substances
(in Greek amorphous means “formless”) do not
have overall regular internal structure; their
constitue...
Curve of cooling of amorphous
substances
0
20
40
60
050100
time, min
To
Curve of cooling of a crystalline
subsatnce
0
10
2...
Definition of Crystal
• A CRYSTAL is a regular polyhedral form,
bounded by smooth faces, which is assumed by
a chemical co...
• A polyhedral form simply means a solid bounded
by flat planes (we call these flat planes
CRYSTAL FACES).
• A chemical co...
Classification of crystals according
to the degree of crystallization
• Euhedral crystals
• Subhedral crystals
• Anhedral ...
External characteristices of crystals
• Crystal faces
• Edge
• Solid angle
• Interfacial angle
• Crystal form
• Crystal ha...
• Crystal faces: The crystal is bounded by
flat plane surfaces. These surfaces
represent the internal arrangement of
atoms...
• Edge: formed by the intersection of any two
adjacent faces.The position in space of an edge
depends upon the position of...
•Interfacial angle
we define the interfacial angle between two crystal
faces as the angle between lines that are perpendic...
Nicholas Steno (1669) a Danish physician and natural
scientist, found that, the angles between similar
crystal faces remai...
• Crystal forms: are a number of corresponding
faces which have the same relation with the
crystallographic axes.
• A crys...
Closed
form
Open
form
• Crystal Habit: the general external shape
of a crystal. It is meant the common and
characteristic form or combination of...
Elements of Crystallization
Crystal Notation
• Crystallographic axis
• Axial angles
Crystallographic axis
• All crystals, with the exception of those
belonging to the hexagonal and trigonal
system, are refe...
Axial angles
• ∝ is the angle between b axis and c axis
• β is the angle between a axis and c axis
• is the angle between ...
Crystal Systems
• We will use our crystallographic axes which we just
discussed to subdivide all known minerals into these...
(2) TETRAGONAL - Three axes, all at right angles, two of
which are equal in length (a and b) and one (c) which is
differen...
• (4) HEXAGONAL - Four axes!
Three of the axes fall in the same plane and
intersect at the axial cross at 120 degrees
betw...
• (5) MONOCLINIC - Three axes, all unequal in
length, two of which (a and c) intersect at an
oblique angle (not 90 degrees...
ELEMENTS OF SYMMETRY
• PLANES OF SYMMETRY
• Rotation AXiS OF SYMMETRY
• CENTER OF SYMMETRY.
PLANE OF SYMMETRY
• Any two dimensional surface (we can call it flat)
that, when passed through the center of the
crystal,...
AXIS OF SYMMETRY
• An imaginary line through the
center of the crystal around
which the crystal may be rotated
so that aft...
four types of axis of symmetry
• When rotation repeats form every 60 degrees, then we
have sixfold or HEXAGONAL SYMMETRY. ...
Types of axis of symmetry
• BINARY SYMMETRY
Two fold system (180º)
Types of axis of symmetry
• TRIGONAL SYMMETRY
Three fold system(120º)
Types of axis of symmetry
• TETRAGONAL SYMMETRY
Four fold system(90º)
Types of axis of symmetry
Six fold system(60º)
HEXAGONAL SYMMETRY
Symmetry Axis of rotary inversion
• This composite symmetry element combines a rotation
about an axis with inversion throu...
CENTER OF SYMMETRY
• Most crystals have a center of
symmetry, even though they
may not possess either planes of
symmetry o...
Complete Symmetrical Formula
• We can use symbol to write the
symmetrical formula as following:
1- Plane of symmetry: m
2-...
Intercepts, Parameters and Indices
• Absolute Intercepts:The distances from
the center of the crystal at which the face
cu...
Parameters
• The parameters of the crystal face are the
intercepts of this face divided by the axes
lengths.
-Parameters
Unit Face
oc
oc:
ob
ob:
oa
oa=
1:1:1
abc
def
2
1
:
3
1
:
4
1
=
oc
of
:
ob
oe
:
oa
od
anm
2:
3
4:
1=
oc
om:
ob
...
Indices
• The Miller indices of a face consist of a series of
whole numbers which have been derived from
the parameters by...
• It is sometimes convenient when the exact
intercepts are unkown to use a general
symbol (hkl) for the miller indices.
c
ba
O
YX
Z
A
B
C
3-D Miller Indices (an unusually complex example)
a b c
unknown face (XYZ)
reference face (ABC)
2
1 4
Mi...
Miller indices
• Always given with 3 numbers
– A, b, c axes
• Larger the Miller index #, closer to the
origin
• Plane para...
What are the Miller Indices of face Z?
b
a
w
(1 1 0)
(2 1 0)
z
The Miller Indices of face z using x as the reference
b
a
w
(1 1 0)
(2 1 0)
z
a b c
unknown face (z)
reference face (x)
1
...
b
a
(1 1 0)
(2 1 0)
(1 0 0)
What do you do with similar faces
on opposite sides of crystal?
b
a
(1 1 0)
(2 1 0)
(1 0 0)
(0 1 0)
(2 1 0)(2 1 0)
(2 1 0)
(1 1 0)(1 1 0)
(1 1 0)
(0 1 0)
(1 0 0)
Methods of Crystal Drawing
• Clingraphic Projection
• Orthogonal Projection
• Spherical Projection
• Stereographic Project...
Clingraphic Projection
Orthogonal Projection
3-Spherical Projection
Imagine that we have a crystal
inside of a sphere. From each
crystal face we draw a line
perpendicu...
4-Stereographic Projection
Stereographic projection is a method used to depict the
angular relationships between crystal f...
For the (011) face we
draw the pole to the
face to intersect the
outside the of the
sphere. Then, we draw
a line from the ...
In the right hand-diagram we see the stereographic projection
for faces of an isometric crystal. Note how the ρ angle is
m...
1- The Primitive Circle is the circle that cross cuts
the sphere and separates it into two equal parts
(North hemisphere a...
4- Mirror planes are shown as solid lines and curves.
The horizontal plane is represented by a circle
match with the primi...
9- The Unit Face (that met with the positive ends of
the three or four crystallographic axes will be
plotted in the lower ...
Crystallographic forms
1- Pedion
It is an open form made up of a single face
Crystallographic forms
1- Pinacoid
It is an open form made up of two parallel faces
Front pinacoid
Side
pinacoid
Basal pin...
Crystallographic forms
3- Dome
It is an open form made up of two
nonparallel faces symmetrical with
respect to a symmetry ...
Crystallographic forms
5- Disphenoid
It is an closed form composed of a four-faced form in which two
faces of the upper sp...
Crystallographic forms
Bipyramid-6
It is an closed form composed of 3, 4, 6, 8 or 12 nonparallel faces
that meet at a poin...
Crystallographic forms
7- Prism
It is an open form composed of 3, 4, 6, 8 or 12 faces, all of which are
parallel to same a...
Crystallographic forms
8- Rhombohedron
It is an closed form composed of 6
rhombohedron faces,
9- Scalenohedron
It is an cl...
Crystallographic systems
Isometric system
β
Ɣ
α
a1 a2
a3
a3a2a1
Ɣ = 90βα
Class
1-Axis of symmetry
3
Isometric system
4
6
2- Center of symmetry
Isometric system
4 vertical plane
3- Plane of symmetry
Isometric system
1 horizontal plane 4 diagonal plane
43
34______
m n
62______
m
Isometric system
Complete Symmetrical Formula
a
b (E)(W)
Stereographic Projection of Symmetry elements of the Isometric System
+
+
+
++
(100)
(010)
(-100)
(0-10)
1- Cube (Hexahedron)
Cubic form [100]
Crystal form
Isometric system
Stereographic Proje...
+
+
+
++
(100)
(010)
(-100)
(0-10)
1- Cube (Hexahedron)
+
++
+
(111)
2- Octahedron
++
+
+
+
Crystal form
Isometric system
...
Crystal form
Isometric system
Rhombic dodecahedron [110]+
+ ++
(100)
(010)10)
1- Cube (Hexahedron)
++
(111)
2- Octahedron
...
Isometric system
Tetrahexahedron [hk0]
+
+
+
++
+
+
+
+
+
+
+
+
+
+
+
(210)
4- Tetrahexahedron
+
+ +
++ +
Stereographic Pr...
Isometric system
Trapezoctahedron [hll] +
++
+
+
++
+
+
+
+
(210)
4- Tetrahexahedron
+
+
+
+ ++
+
++ +
+
+
(211)
6-Trapezo...
Trisoctahedron [hhl]
Isometric system
+
+
+
++
+
+
+
+
+
+
+
+
+
+
+
(210)
4- Tetrahexahedron
+
++
+
+
+
+
+
+
+
+
+
(221)...
Hexaoctahedron [hkl]
Isometric system
+
++
+
+
(210)
4- Tetrahexahedron
++ ++ (221)
5- Trisoctahedron
+
+
+
+ ++
+
++ +
+
...
systemTetragonal
β
Ɣ
α
ca2a1 /
c
a1 a2
Ɣ = 90βα
Ditetragonal –
Bipyramid [hkl]
Class
1
4
systemTetragonal
1-Axis of symmetry
systemTetragonal
2- Center of symmetry
systemTetragonal
3- Plane of symmetry
4 vertical plane
1 horizontal plane
4______
m
42______
m
n
systemTetragonal
Complete Symmetrical Formula
Stereographic Projection of Symmetry elements of the Tetragonal System
a
b (E)(W)
Basal - pinacoid [001]
systemTetragonalCrystal form
+
1- Basal Pinacoid
(001)
(00-1)
Stereographic Projection
Tetragonal prism of
first order [110]
systemTetragonal
+
1- Basal Pinacoid
(001)
(00-1)
2- Tetragonal prism of 1st order
+...
Tetragonal prism of
second order [100]
systemTetragonal
ographic projection of Tetragonal
em Forms.
+
1- Basal Pinacoid
(0...
Ditetragonal prism [hk0]
systemTetragonal
4- Ditetragonal prism
+
+
+
++
+
+
+
(210)
a
b
5-
b
+
+
++
+
+
Stereographic Pro...
systemTetragonal
Tetragonal – Bipyramid
of first order [hhl]
4- Ditetragonal prism
+
+
+
++
+
+
+
(210)
a
b
5- Tetragonal ...
systemTetragonal
Tetragonal – Bipyramid
of second order [h0l]
4- Ditetragonal prism
+
++
+
(210)
a
b
5- Tetragonal bipyram...
systemTetragonal
Ditetragonal –
Bipyramid [hkl]
4- Ditetragonal prism
+
++
+
(210)
a
b
5- T
7- Ditetragonal bipyramid
a
b
...
Compound form
Orthorhombic system
β
Ɣ
α
cba / /
c
a b
Ɣ = 90βα
Orthorhombic Bipyramid [hkl]
Class
7- Orthorhom bic Bipyram id {hkl}
 Exit
hkl
It is a closed form
com poses of 8 triangular
faces. It is the general
form o...
3
1-Axis of symmetry
Orthorhombic system
2- Center of symmetry
3- Plane of symmetry
2 vertical plane 1 horizontal plane
32______
m n
Orthorhombic system
Complete Symmetrical Formula
Stereographic Projection of Symmetry elements of the Orthorhombic
System.
a
b (E)(W)
Orthorhombic system
Crystal form
Side
pinacoid
[010]
Front pinacoid [100]
Basal Pinacoid [001]
1- Basal Pinacoid
a
b+
2- F...
Orthorhombic prism [hk0]
Orthorhombic system
4- Orthorhombic prism
a
b
+
++
+ (110)
b
++
Stereographic Projection
Orthorhombic system
Orthorhombic front dome [h0l]
4- Orthorhombic prism
a
b
+
++
+ (110)
5- Front dome (b-Dome)
a
b
+
+
(1...
Orthorhombic side dome [0kl]
Orthorhombic system
4- Orthorhombic prism
a
b
++ (110)
5- Front dome (b-Dome)
a
b
+
+
(101)
6...
Orthorhombic Bipyramid [hkl]
Orthorhombic system
4- Orthorhombic prism
a
b
++ (110)
7- orthorhombic bipyramid
a
b
+
++
+
S...
Compound form
5- O rthorhom bic front dom e (b-dom e) or M acro
dom e {10l}
6- O rthorhom bic side dom e (a-dom e) or Brac...
Hexagonal system
/ca3a2a1
a1
a2
-a
3
c
Ɣ
β α
90βα
Ɣ
Class
Dihexagonal bipyramid [hkwl]
61
Hexagonal system
1-Axis of symmetry 2- Center of symmetry
3- Plane of symmetry
Hexagonal system
6 vertical plane 1 horizontal plane
Apatite
Ca5(PO4)3(OH, Cl,F)
-hexagonal structure
-prismatic habit
-major component teeth
6______
m
62______
m
n
Complete Symmetrical Formula
Hexagonal system
a1
a2 (E)(W)
Stereographic Projection of Symmetry elements of the Hexagonal System
-a3
Hexagonal prism of
first order [1010]
-1010
-
a1
-a3 a2
0001
Hexagonal system
Crystal form
Basal pinacoid [0001]
Stereogra...
hhw0
-
a1
-a
3
a2
Hexagonal systemHexagonal prism of
second order [hhw0]
-
Stereographic projection of the Hexagonal
Syste...
hkw0
-
Hexagonal system-Dihexagonal prism [hkw0]
Stereographic Projection
a1
a2
-a3
4- Hexagonal Bipyramid of first order
...
Hexagonal Bipyramid of
first order [h0hl]
-
h0hl
-
a1
-a3
a2
Hexagonal system
a1
a2
-a3
4- Hexagonal Bipyramid of first or...
Hexagonal Bipyramid of
second order [hhwl]
-
hhwl
-
a1 -a3
a2
Hexagonal system
a1
a2
-a3
4- Hexagonal Bipyramid of first o...
Dihexagonal bipyramid [hkwl]
-
hkwl
-
Hexagonal system
Stereographic Projection
a1
a2
-a3
4- Hexagonal Bipyramid of first ...
Compound form
Hexagonal prism (m = 6)
Hexagonal bipyramid (m = 12)
Trigonal system
Ɣ
β α
a1
a2
-a3
c
/ ca3a2a1
90βα
120Ɣ
ditrigonal scalenohedron
Class
31
Trigonal system
1-Axis of symmetry 2- Center of symmetry
Trigonal system
3- Plane of symmetry
3 vertical plane
______
32
m n3
Trigonal system
Complete Symmetrical Formula
a1
a2 (E)(W)
Stereographic Projection of Symmetry elements of the Triagonal System
-a3
Forms
Basal Pinacoid
First Order Prism
Second Order Prism
Dihexagonal prism
Second Order bipyramid
Trigonal rhombohedron
D...
Positive trigonal
rhombohedron [h0hl]
-
h0hl
-
a1 -a3
a2
Trigonal system
Crystal form
a1 -a3
a2
Positive rhombohedron {10-...
Negative trigonal
rhombohedron [0kkl]
-
0kkl
-
a1 -a
3
a2
Trigonal system
a1 -a3
a2
a1 -a3
a2
Positive rhombohedron {10-11...
Positive ditrigonal
scalenohedron [hkwl]
-
hkwl
-
a1 -a3
a2
Trigonal system
Stereographic projection of the Tr
a1 -a3
Posi...
Negative ditrigonal
scalenohedron [hkwl]
-
hkwl
-
a1 -a3
a2
Trigonal system
Stereographic projection of the Triagonal Syst...
Monoclinic system
90Ɣα
cba / /
β 90/
c
a b
β
Ɣ
α
Class
1
Monoclinic system
1-Axis of symmetry 2- Center of symmetry
Monoclinic system
3- Plane of symmetry
1 vertical plane
2______
m n
Monoclinic system
Complete Symmetrical Formula
Stereographic Projection of Symmetry elements of the Monoclinic System
a
b (E)(W)
Monoclinic front pinacoid [100]
Monoclinic side pinacoid [010]
Monoclinic basal pinacoid [001]
Monoclinic system
Stereogra...
Monoclinic prism [hk0]
Monoclinic system
Stereographic Projection
m {hk0} or {110}
4- Monoclinic Prism
a
+
++
+
++
(-111)
Positive hemibipyramid [hkl]
Monoclinic system
Positive Hemibipyramid {hkl} or {111}
Negative Hemibipyramid {-hkl} or {-11...
5- Side Dome (a-dome)4- Monoclinic Prism
a
+
+
a
++
a a
+ (101)
+(-101)
++
(111)
+
(-111)
-
011
Monoclinic system
• Dome
-...
Triclinic system
cba / /
c
a
b
β
Ɣ
α
/α β Ɣ 90//
Class
Pinacoid
Triclinic system
1-Axis of symmetry = -
2- Center of symmetry = n
3- Plane of symmetry = -
n
Triclinic system
Complete Symmetrical Formula
Stereographic Projection of Symmetry elements of the Triclinic System
front pinacoid [100]
side pinacoid [010]
basal pinacoid [001]
Triclinic system
Crystal form
Stereographic projection of th...
Right hemi-prism [hk0]
Left hemi-prism [hk0]
Triclinic system
-
a a a a
a a
a a
a a
+
+
+
+
+
+ +
+ +
5- Hemi-b-dome {h0l}...
Hemi-brachydome(0kl) Hemi-macrodome(h0l)
Triclinic system
a a a a
+ +
+
+
5- Hemi-b-dome {h0l}: two forms
{101} and {-101}...
Upper right quarter bipyramid [hkl]
Upper left quarter bipyramid [hkl]
Lower right quarter bipyramid [hkl]
Lower left quar...
Crystal Morphology
• The angular relationships, size and shape of
faces on a crystal
• Bravais Law – crystal faces will mo...
Unit Cell Types
in Bravais Lattices
P – Primitive; nodes at
corners only
C – Side-centered; nodes
at corners and in
center...
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
An Introduction to Crystallography
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An Introduction to Crystallography

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An Introduction to Crystallography, Elements of crystals crystal systems: Cubic (Isometric) System,Tetragonal System, Orthorhombic System, Hexagonal System; Trigonal System, Monoclinic System, Triclinic System

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  • DOWNLOAD FULL BOOKS, INTO AVAILABLE FORMAT ......................................................................................................................... ......................................................................................................................... 1.DOWNLOAD FULL. PDF eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. doc eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. PDF eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. doc eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .............. Browse by Genre Available eBooks ......................................................................................................................... Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Crime, eBooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult,
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  • DOWNLOAD FULL BOOKS, INTO AVAILABLE FORMAT ......................................................................................................................... ......................................................................................................................... 1.DOWNLOAD FULL. PDF EBOOK here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB Ebook here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... 1.DOWNLOAD FULL. doc Ebook here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... 1.DOWNLOAD FULL. PDF EBOOK here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB Ebook here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... 1.DOWNLOAD FULL. doc Ebook here { https://tinyurl.com/y8nn3gmc } ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .............. Browse by Genre Available eBooks ......................................................................................................................... Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult,
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An Introduction to Crystallography

  1. 1. An Introduction to Crystallography
  2. 2. CONTENTSCrystallography:  Why we study Crystallography?  Definition  External characteristics of crystals • Elements of crystals  Crystal elements  Crystal symmetry  Crystal systems  Crystal classes  Axial ratios-crystal parameters and Miller indices  Methods of Crystal Drawing  Crystal habit and forms • General Outlines of the crystal systems  Cubic (Isometric) System  Tetragonal System  Orthorhombic System  Hexagonal System  Trigonal System  Monoclinic System  Triclinic System
  3. 3.  Atomic structure  Central region called the nucleus  Consists of protons (+ charges) and neutrons (- charges)  Electrons  Negatively charged particles that surround the nucleus  Located in discrete energy levels called shells
  4. 4.  Chemical bonding  Formation of a compound by combining two or more elements  Ionic bonding  Atoms gain or lose outermost (valence) electrons to form ions  Ionic compounds consist of an orderly arrangement of oppositely charged ions
  5. 5.  Covalent bonding  Atoms share electrons to achieve electrical neutrality  Generally stronger than ionic bonds  Both ionic and covalent bonds typically occur in the same compound
  6. 6. Covalent bond Model - diamond (Carbon)
  7. 7.  Polymorphs  Minerals with the same composition but different crystalline structures  Examples include diamond and graphite  Phase change = one polymorph changing into another
  8. 8.  Crystal form  External expression of a mineral’s internal structure  Often interrupted due to competition for space and rapid loss of heat
  9. 9. Why we study Crystallography? It is useful for the identification of minerals. The later are chemical substances formed under natural conditions and have crystal forms.
  10. 10. Study of crystals can provide new chemical information. In laboratories and industry, we can prepare pure chemical substances by crystallization process. It is very useful for solid state studies of materials. Crystal heating therapy Crystallography is of major importance to a wide range of scientific disciplines including physics, chemistry, molecular biology, materials science and mineralogy.
  11. 11. DEFINITION • CRYSTALLOGRAPHY is simply a fancy word meaning "the study of crystals" • The study of crystalline solids and the principles that govern their growth, external shape, and internal structure • Crystallography is easily divided into 3 sections - - geometrical, physical, and chemical. • We will cover the most significant geometric aspects of crystallography
  12. 12. Classification of substances • Crystalline Substances • Amorphous substances
  13. 13. Properties of Crystalline Substances 1- Solidity 2- Anisotropy X Isotropy 3- Self-faceting ability 4- Symmetry space lattice skeleton The crystalline substances are characterise by the following properties:
  14. 14. Amorphous substances (in Greek amorphous means “formless”) do not have overall regular internal structure; their constituent particles are arranged randomly; hence, they are isotropic, have no symmetry, and cannot be bounded by faces. Particles are arranged in them in the same way as in liquids, hence, they are sometimes referred to as supercooled liquids. Examples of amorphous substances are glass, plastics. Glue, resin, and solidified colloids (gels).
  15. 15. Curve of cooling of amorphous substances 0 20 40 60 050100 time, min To Curve of cooling of a crystalline subsatnce 0 10 20 30 40 50 60 050100 time, min To ab In distinction to crystalline substances, amorphous ones have no clearly defined melting point. Comparing curves of cooling (or heating) of crystalline substances and amorphous substances, one can see that the former has two sharp bend-points (a and b), corresponding to the beginning and end crystallization respectively, whereas the latter is smooth.
  16. 16. Definition of Crystal • A CRYSTAL is a regular polyhedral form, bounded by smooth faces, which is assumed by a chemical compound, due to the action of its interatomic forces, when passing, under suitable conditions, from the state of a liquid or gas to that of a solid.
  17. 17. • A polyhedral form simply means a solid bounded by flat planes (we call these flat planes CRYSTAL FACES). • A chemical compound" tells us that all minerals are chemicals, just formed by and found in nature. • The last half of the definition tells us that a crystal normally forms during the change of matter from liquid or gas to the solid state.
  18. 18. Classification of crystals according to the degree of crystallization • Euhedral crystals • Subhedral crystals • Anhedral crystals Euhedral Crystal Subhedral Crystal Anhedral Crystal
  19. 19. External characteristices of crystals • Crystal faces • Edge • Solid angle • Interfacial angle • Crystal form • Crystal habit
  20. 20. • Crystal faces: The crystal is bounded by flat plane surfaces. These surfaces represent the internal arrangement of atoms and usually parallel to net-planes containing the greatest number of lattice- points or ions. • Faces are two kinds, like and unlike.
  21. 21. • Edge: formed by the intersection of any two adjacent faces.The position in space of an edge depends upon the position of the faces whose intersection gives rise to it. • Solid Angles: formed by intersection of three or more faces. A F E Edges………….E Solid Angles (apices)…..A Crystal Faces….F Can you conclude mathematical relation between them?
  22. 22. •Interfacial angle we define the interfacial angle between two crystal faces as the angle between lines that are perpendicular to the faces. Such lines are called the poles to the crystal face. Note that this angle can be measured easily with a device called a contact goniometer.
  23. 23. Nicholas Steno (1669) a Danish physician and natural scientist, found that, the angles between similar crystal faces remain constant regardless of the size or the shape of the crystal when measured at the same temperature, So whether the crystal grew under ideal conditions or not, if you compare the angles between corresponding faces on various crystals of the same mineral, the angle remains the same Steno's law is called the CONSTANCY OF INTERFACIAL ANGLES and, like other laws of physics and chemistry, we just can't get away from it.
  24. 24. • Crystal forms: are a number of corresponding faces which have the same relation with the crystallographic axes. • A crystal made up entirely of like faces is termed a simple form. A crystal which consists of two or more simple forms is called combination. • Closed form: simple form occurs in crystal as it can enclose space. • Open form: simple forms can only occur in combination in crystal •The term general form has specific meaning in crystallography. In each crystal class, there is a form in which the faces intersect each crytallographic axes at different lengths. This is the general form {hkl} and is the name for each of the 32 classes (hexoctahedral class of the isometric system, for example). All other forms are called special forms.
  25. 25. Closed form Open form
  26. 26. • Crystal Habit: the general external shape of a crystal. It is meant the common and characteristic form or combination of forms in which a mineral crystallizes.(Tabular habit, Platy habit, Prismatic habit, Acicular habit, Bladed habit)
  27. 27. Elements of Crystallization Crystal Notation • Crystallographic axis • Axial angles
  28. 28. Crystallographic axis • All crystals, with the exception of those belonging to the hexagonal and trigonal system, are referred to three crystallographic axis.
  29. 29. Axial angles • ∝ is the angle between b axis and c axis • β is the angle between a axis and c axis • is the angle between a axis and b axis
  30. 30. Crystal Systems • We will use our crystallographic axes which we just discussed to subdivide all known minerals into these systems. The systems are: (1) CUBIC (ISOMETRIC) - The three crystallographic axes are all equal in length and intersect at right angles (90 degrees) to each other. β Ɣ α a1 a2 a3
  31. 31. (2) TETRAGONAL - Three axes, all at right angles, two of which are equal in length (a and b) and one (c) which is different in length (shorter or longer). (3) ORTHORHOMBIC - Three axes, all at right angles, and all three of different lengths. β Ɣ α c a1 a2 β Ɣ α c a b TETRAGONAL ORTHORHOMBIC
  32. 32. • (4) HEXAGONAL - Four axes! Three of the axes fall in the same plane and intersect at the axial cross at 120 degrees between the positive ends. These 3 axes, labeled a1, a2, and a3, are the same length. The fourth axis, termed c, may be longer or shorter than the a axes set.
  33. 33. • (5) MONOCLINIC - Three axes, all unequal in length, two of which (a and c) intersect at an oblique angle (not 90 degrees), the third axis (b) is perpendicular to the other two axes. • (6) TRICLINIC - The three axes are all unequal in length and intersect at three different angles (any angle but 90 degrees). c a b β Ɣ α c a b β Ɣ α MONOCLINIC TRICLINIC
  34. 34. ELEMENTS OF SYMMETRY • PLANES OF SYMMETRY • Rotation AXiS OF SYMMETRY • CENTER OF SYMMETRY.
  35. 35. PLANE OF SYMMETRY • Any two dimensional surface (we can call it flat) that, when passed through the center of the crystal, divides it into two symmetrical parts that are MIRROR IMAGES is a PLANE OF SYMMETRY. • In other words, such a plane divides the crystal so that one half is the mirror-image of the other. Horizontal planeVertical planeDiagonal plane
  36. 36. AXIS OF SYMMETRY • An imaginary line through the center of the crystal around which the crystal may be rotated so that after a definite angular revolution the crystal form appears the same as before is termed an axis of symmetry. • Depending on the amount or degrees of rotation necessary, four types of axes of symmetry are possible when you are considering crystallography
  37. 37. four types of axis of symmetry • When rotation repeats form every 60 degrees, then we have sixfold or HEXAGONAL SYMMETRY. A filled hexagon symbol is noted on the rotational axis. • When rotation repeats form every 90 degrees, then we have fourfold or TETRAGONAL SYMMETRY. A filled square is noted on the rotational axis. • When rotation repeats form every 120 degrees, then we have threefold or TRIGONAL SYMMETRY. A filled equilateral triangle is noted on the rotational axis. • When rotation repeats form every 180 degrees, then we have twofold or BINARY SYMMETRY. A filled oval is noted on the rotational axis.
  38. 38. Types of axis of symmetry • BINARY SYMMETRY Two fold system (180º)
  39. 39. Types of axis of symmetry • TRIGONAL SYMMETRY Three fold system(120º)
  40. 40. Types of axis of symmetry • TETRAGONAL SYMMETRY Four fold system(90º)
  41. 41. Types of axis of symmetry Six fold system(60º) HEXAGONAL SYMMETRY
  42. 42. Symmetry Axis of rotary inversion • This composite symmetry element combines a rotation about an axis with inversion through the center. • There may be 1, 2, 3, 4, and 6-fold rotary inversion axes present in natural crystal forms, depending upon the crystal system we are discussing. - - - -
  43. 43. CENTER OF SYMMETRY • Most crystals have a center of symmetry, even though they may not possess either planes of symmetry or axes of symmetry. Triclinic crystals usually only have a center of symmetry. If you can pass an imaginary line from the surface of a crystal face through the center of the crystal (the axial cross) and it intersects a similar point on a face equidistance from the center, then the crystal has a center of symmetry.
  44. 44. Complete Symmetrical Formula • We can use symbol to write the symmetrical formula as following: 1- Plane of symmetry: m 2- Axis of symmetry: 2, 3, 4, 6 and we can write the number of the axis at up left as 3 4 3- Center of symmetry: n For example: the complete symmetrical formula of hexoctahedral class of Isometric system: 3 4/m 4 3 6 2/m n
  45. 45. Intercepts, Parameters and Indices • Absolute Intercepts:The distances from the center of the crystal at which the face cuts the crystallographic axes. • Relative Intercepts: divided the absolute intercepts by the intercept of the face with b axis. • Ex: if the absolute intercepts (a:b:c)are 1mm : 2mm : ½ mm, the relative intercepts will be ½ : 2/2 : ¼ = o.5 : 1 : o.25
  46. 46. Parameters • The parameters of the crystal face are the intercepts of this face divided by the axes lengths.
  47. 47. -Parameters Unit Face oc oc: ob ob: oa oa= 1:1:1 abc def 2 1 : 3 1 : 4 1 = oc of : ob oe : oa od anm 2: 3 4: 1= oc om: ob on: oa oa If the face parallel to the axis, Its intercept = ∞ Its Parameter=∞
  48. 48. Indices • The Miller indices of a face consist of a series of whole numbers which have been derived from the parameters by their inversion and if necessary the subsequent clearing of fractions. • If the parameters are 111 so the indices will be 111 • If the parameters are 11∞ and on inversion 1/1, 1/1, 1/ ∞ woud have (110) for indices. • Faces which have respectively the parameters 1, 1, ½ would on inversion yield 1/1, 1/1, 2/1 thus on clearing of fractions the resulting indices would be respectively (112)
  49. 49. • It is sometimes convenient when the exact intercepts are unkown to use a general symbol (hkl) for the miller indices.
  50. 50. c ba O YX Z A B C 3-D Miller Indices (an unusually complex example) a b c unknown face (XYZ) reference face (ABC) 2 1 4 Miller index of face XYZ using ABC as the reference face 3 invert 1 2 4 3 clear of fractions (1 3)4
  51. 51. Miller indices • Always given with 3 numbers – A, b, c axes • Larger the Miller index #, closer to the origin • Plane parallel to an axis, intercept is 0
  52. 52. What are the Miller Indices of face Z? b a w (1 1 0) (2 1 0) z
  53. 53. The Miller Indices of face z using x as the reference b a w (1 1 0) (2 1 0) z a b c unknown face (z) reference face (x) 1 1 1 Miller index of face z using x (or any face) as the reference face 1 invert 1 1 1 1 clear of fractions 1 00 (1 0 0)
  54. 54. b a (1 1 0) (2 1 0) (1 0 0) What do you do with similar faces on opposite sides of crystal?
  55. 55. b a (1 1 0) (2 1 0) (1 0 0) (0 1 0) (2 1 0)(2 1 0) (2 1 0) (1 1 0)(1 1 0) (1 1 0) (0 1 0) (1 0 0)
  56. 56. Methods of Crystal Drawing • Clingraphic Projection • Orthogonal Projection • Spherical Projection • Stereographic Projection
  57. 57. Clingraphic Projection
  58. 58. Orthogonal Projection
  59. 59. 3-Spherical Projection Imagine that we have a crystal inside of a sphere. From each crystal face we draw a line perpendicular to the face (poles to the face). Note that the angle is measured in the vertical plane containing the c axis and the pole to the face, and the angle is measured in the horizontal plane, clockwise from the b axis. The pole to a hypothetical (010) face will coincide with the b crystallographic axis, and will impinge on the inside of the sphere at the equator.
  60. 60. 4-Stereographic Projection Stereographic projection is a method used to depict the angular relationships between crystal faces. This time, however we will first look at a cross- section of the sphere as shown in the diagram. We orient the crystal such that the pole to the (001) face (the c axis) is vertical and points to the North pole of the sphere. N EW (010) (001) (011) (0-10) (0-11) ρ ρ/2 Imagine that we have a crystal inside of a sphere.
  61. 61. For the (011) face we draw the pole to the face to intersect the outside the of the sphere. Then, we draw a line from the point on the sphere directly to the South Pole of the sphere. N EW (010) (001) (011) (0-10) (0-11) ρ ρ/2 Where this line intersects the equatorial plane is where we plot the point. The stereographic projection then appears on the equatorial plane.
  62. 62. In the right hand-diagram we see the stereographic projection for faces of an isometric crystal. Note how the ρ angle is measured as the distance from the center of the projection to the position where the crystal face plots. The Φ angle is measured around the circumference of the circle, in a clockwise direction away from the b crystallographic axis or the plotting position of the (010) crystal face N EW (010) (001) (011) (0-10) (0-11) ρ ρ/2 EW (010) (001) (0-10) (011)(0-11) ρ
  63. 63. 1- The Primitive Circle is the circle that cross cuts the sphere and separates it into two equal parts (North hemisphere and South hemisphere). It is drawn as solid circle when represents a mirror plane. The following rules are applied: 2- All crystal faces are plotted as poles (lines perpendicular to the crystal face. Thus, angles between crystal faces are really angles between poles to crystal faces. 3- The b crystallographic axis is taken as the starting point. Such an axis will be perpendicular to the (010) crystal face in any crystal system. The [010] axis (note zone symbol) or (010) crystal face will therefore plot at Φ = 0° and ρ = 90°.
  64. 64. 4- Mirror planes are shown as solid lines and curves. The horizontal plane is represented by a circle match with the primitive circle. 5- Crystal faces that are on the top of the crystal ρ < 90°) will be plotted as "+" signs, and crystal faces on the bottom of the crystal (ρ > 90°) will be plotted as open circles “ " . 6- The poles faces that parallel to the c crystallographic axis lie on the periphery of the primitive circle and is plotted as "+" signs. 7- The poles faces that perpendicular to the c crystallographic axis lie on the center of the primitive circle. 8- The pole face parallels to one of the horizontal axes will plotted on the plane that perpendiculars to this axis.
  65. 65. 9- The Unit Face (that met with the positive ends of the three or four crystallographic axes will be plotted in the lower right quarter of the primitive circle. a b ++ - + + - - - As an example all of the faces, both upper and lower, for a crystal in the class 4/m2/m in the forms {100} (hexahedron, 6 faces) and {110} (dodecahedron, 12 faces) are in the stereogram to the right + (001)(00-1) + ++ + + (100) (-100) (010)(0-10) + ++ ++ + + (-110) (-1-10) (110)(1-10) (101)(10-1) (011)(01-1)(0-11)(0-1-1) (-101)(-10-1)
  66. 66. Crystallographic forms 1- Pedion It is an open form made up of a single face
  67. 67. Crystallographic forms 1- Pinacoid It is an open form made up of two parallel faces Front pinacoid Side pinacoid Basal pinacoid
  68. 68. Crystallographic forms 3- Dome It is an open form made up of two nonparallel faces symmetrical with respect to a symmetry plane 4- Sphenoid It is an open form made up of two nonparallel faces symmetrical with respect to a 2-fold or 4-fold symmetry axis
  69. 69. Crystallographic forms 5- Disphenoid It is an closed form composed of a four-faced form in which two faces of the upper sphenoid alternate with two of the lower sphenoid.
  70. 70. Crystallographic forms Bipyramid-6 It is an closed form composed of 3, 4, 6, 8 or 12 nonparallel faces that meet at a point Orthorhombic bipyramed Ditetragonal bipyramid Tetragonal bipyramid Dihexagonal bipyramidHexagonal bipyramid
  71. 71. Crystallographic forms 7- Prism It is an open form composed of 3, 4, 6, 8 or 12 faces, all of which are parallel to same axis. Orthorhombic prism Tetragonal prism Ditetragonal prism Hexagonal prism Dihexagonal prism
  72. 72. Crystallographic forms 8- Rhombohedron It is an closed form composed of 6 rhombohedron faces, 9- Scalenohedron It is an closed form composed of 12 faces, each face is a scalene triangle. There are three pairs of faces above and three pairs below in alternating positions
  73. 73. Crystallographic systems Isometric system β Ɣ α a1 a2 a3 a3a2a1 Ɣ = 90βα Class
  74. 74. 1-Axis of symmetry 3 Isometric system 4 6
  75. 75. 2- Center of symmetry Isometric system
  76. 76. 4 vertical plane 3- Plane of symmetry Isometric system 1 horizontal plane 4 diagonal plane
  77. 77. 43 34______ m n 62______ m Isometric system Complete Symmetrical Formula
  78. 78. a b (E)(W) Stereographic Projection of Symmetry elements of the Isometric System
  79. 79. + + + ++ (100) (010) (-100) (0-10) 1- Cube (Hexahedron) Cubic form [100] Crystal form Isometric system Stereographic Projection
  80. 80. + + + ++ (100) (010) (-100) (0-10) 1- Cube (Hexahedron) + ++ + (111) 2- Octahedron ++ + + + Crystal form Isometric system Octahedron [111] Stereographic Projection
  81. 81. Crystal form Isometric system Rhombic dodecahedron [110]+ + ++ (100) (010)10) 1- Cube (Hexahedron) ++ (111) 2- Octahedron + ++ + + + + + (110) 3- Rhombic dodecahedron ereographic projection of Cubic System rms. Stereographic Projection
  82. 82. Isometric system Tetrahexahedron [hk0] + + + ++ + + + + + + + + + + + (210) 4- Tetrahexahedron + + + ++ + Stereographic Projection
  83. 83. Isometric system Trapezoctahedron [hll] + ++ + + ++ + + + + (210) 4- Tetrahexahedron + + + + ++ + ++ + + + (211) 6-Trapezohedron Stereographic Projection
  84. 84. Trisoctahedron [hhl] Isometric system + + + ++ + + + + + + + + + + + (210) 4- Tetrahexahedron + ++ + + + + + + + + + (221) 5- Trisoctahedron + + + + + ++ + + + + + Stereographic Projection
  85. 85. Hexaoctahedron [hkl] Isometric system + ++ + + (210) 4- Tetrahexahedron ++ ++ (221) 5- Trisoctahedron + + + + ++ + ++ + + + (211) 6-Trapezohedron + + +++ + + + ++ ++ + + + ++ + + + + +++ (321) 7- Hexaoctahedron Stereographic Projection
  86. 86. systemTetragonal β Ɣ α ca2a1 / c a1 a2 Ɣ = 90βα Ditetragonal – Bipyramid [hkl] Class
  87. 87. 1 4 systemTetragonal 1-Axis of symmetry
  88. 88. systemTetragonal 2- Center of symmetry
  89. 89. systemTetragonal 3- Plane of symmetry 4 vertical plane 1 horizontal plane
  90. 90. 4______ m 42______ m n systemTetragonal Complete Symmetrical Formula
  91. 91. Stereographic Projection of Symmetry elements of the Tetragonal System a b (E)(W)
  92. 92. Basal - pinacoid [001] systemTetragonalCrystal form + 1- Basal Pinacoid (001) (00-1) Stereographic Projection
  93. 93. Tetragonal prism of first order [110] systemTetragonal + 1- Basal Pinacoid (001) (00-1) 2- Tetragonal prism of 1st order + ++ + (110) + + + Stereographic Projection
  94. 94. Tetragonal prism of second order [100] systemTetragonal ographic projection of Tetragonal em Forms. + 1- Basal Pinacoid (001) (00-1) 2- Tetragonal prism of 1st order + ++ + (110) 3- Tetragonal Prism of 2nd Order + + + + (100) Stereographic Projection
  95. 95. Ditetragonal prism [hk0] systemTetragonal 4- Ditetragonal prism + + + ++ + + + (210) a b 5- b + + ++ + + Stereographic Projection
  96. 96. systemTetragonal Tetragonal – Bipyramid of first order [hhl] 4- Ditetragonal prism + + + ++ + + + (210) a b 5- Tetragonal bipyramid of 1st Order a b + ++ + + + ++ + (111) Stereographic Projection
  97. 97. systemTetragonal Tetragonal – Bipyramid of second order [h0l] 4- Ditetragonal prism + ++ + (210) a b 5- Tetragonal bipyramid of 1st Order a b ++ 6- Tetragonal bipyramid of 2nd Order a b + + + + 7- Ditetragonal bipyramid a b + + + ++ + + + (111) (101) (211) Stereographic Projection
  98. 98. systemTetragonal Ditetragonal – Bipyramid [hkl] 4- Ditetragonal prism + ++ + (210) a b 5- T 7- Ditetragonal bipyramid a b + + + ++ + + + (211) Stereographic Projection
  99. 99. Compound form
  100. 100. Orthorhombic system β Ɣ α cba / / c a b Ɣ = 90βα Orthorhombic Bipyramid [hkl] Class
  101. 101. 7- Orthorhom bic Bipyram id {hkl}  Exit hkl It is a closed form com poses of 8 triangular faces. It is the general form of the orthorhom bic holosym m etrical class. Each face m et with the crystallographic axes at different distances {111} or {hkl}.
  102. 102. 3 1-Axis of symmetry Orthorhombic system 2- Center of symmetry 3- Plane of symmetry 2 vertical plane 1 horizontal plane
  103. 103. 32______ m n Orthorhombic system Complete Symmetrical Formula
  104. 104. Stereographic Projection of Symmetry elements of the Orthorhombic System. a b (E)(W)
  105. 105. Orthorhombic system Crystal form Side pinacoid [010] Front pinacoid [100] Basal Pinacoid [001] 1- Basal Pinacoid a b+ 2- Front Pi a b + + (100) (001) b++ (010) Stereographic projection of the Orthorhombic System Forms. 1- Basal Pinacoid a b+ 2- Front Pinacoid a b + + (100) (001) 3- Side Pinacoid a b++ (010) Stereographic Projection
  106. 106. Orthorhombic prism [hk0] Orthorhombic system 4- Orthorhombic prism a b + ++ + (110) b ++ Stereographic Projection
  107. 107. Orthorhombic system Orthorhombic front dome [h0l] 4- Orthorhombic prism a b + ++ + (110) 5- Front dome (b-Dome) a b + + (101) bb ++ Stereographic Projection
  108. 108. Orthorhombic side dome [0kl] Orthorhombic system 4- Orthorhombic prism a b ++ (110) 5- Front dome (b-Dome) a b + + (101) 6- Side dome (a-Dome) a b++ (011) 7- orthorhombic bipyramid a b + ++ + Stereographic Projection
  109. 109. Orthorhombic Bipyramid [hkl] Orthorhombic system 4- Orthorhombic prism a b ++ (110) 7- orthorhombic bipyramid a b + ++ + Stereographic Projection
  110. 110. Compound form 5- O rthorhom bic front dom e (b-dom e) or M acro dom e {10l} 6- O rthorhom bic side dom e (a-dom e) or Brachy dom e {01l} 01l 01l10l 100 Pinacoid
  111. 111. Hexagonal system /ca3a2a1 a1 a2 -a 3 c Ɣ β α 90βα Ɣ Class Dihexagonal bipyramid [hkwl]
  112. 112. 61 Hexagonal system 1-Axis of symmetry 2- Center of symmetry
  113. 113. 3- Plane of symmetry Hexagonal system 6 vertical plane 1 horizontal plane
  114. 114. Apatite Ca5(PO4)3(OH, Cl,F) -hexagonal structure -prismatic habit -major component teeth
  115. 115. 6______ m 62______ m n Complete Symmetrical Formula Hexagonal system
  116. 116. a1 a2 (E)(W) Stereographic Projection of Symmetry elements of the Hexagonal System -a3
  117. 117. Hexagonal prism of first order [1010] -1010 - a1 -a3 a2 0001 Hexagonal system Crystal form Basal pinacoid [0001] Stereographic projection of the Hexagonal System Forms. a1 a2 -a3 + 1- Hexagonal Pinacoid (0001) a1 a2 -a3 2- Hexagonal prism of first order (10-10) + + + + + + a1 a2 -a3 3- Hexagonal prism of second order + + ++ + + (11-20) Stereographic Projection
  118. 118. hhw0 - a1 -a 3 a2 Hexagonal systemHexagonal prism of second order [hhw0] - Stereographic projection of the Hexagonal System Forms. a1 -a3 1- Hexagonal Pinacoid a1 -a3 2- Hexagonal prism of first order (10-10) + ++ a1 a2 -a3 3- Hexagonal prism of second order + + ++ + + (11-20) Stereographic Projection
  119. 119. hkw0 - Hexagonal system-Dihexagonal prism [hkw0] Stereographic Projection a1 a2 -a3 4- Hexagonal Bipyramid of first order + (10-11) ++ a1 a2 -a3 6- Dihexagonal prism (21-30) + + + + + ++ + + + + +
  120. 120. Hexagonal Bipyramid of first order [h0hl] - h0hl - a1 -a3 a2 Hexagonal system a1 a2 -a3 4- Hexagonal Bipyramid of first order + (10-11) + + + + + a1 a2 + + + + + ++ + + + + + Stereographic Projection
  121. 121. Hexagonal Bipyramid of second order [hhwl] - hhwl - a1 -a3 a2 Hexagonal system a1 a2 -a3 4- Hexagonal Bipyramid of first order + (10-11) + + + + + a1 a2 -a3 5- Hexagonal Bipyramid of second order + (11-21) + ++ + + a2 + + ++ + + + a2 + + ++ + + Stereographic Projection
  122. 122. Dihexagonal bipyramid [hkwl] - hkwl - Hexagonal system Stereographic Projection a1 a2 -a3 4- Hexagonal Bipyramid of first order + (10-11) ++ a1 a2 -a3 5- Hexagonal Bipyramid of second order + (11-21) ++ + a1 a2 -a3 6- Dihexagonal prism (21-30) + + + + + ++ + + + + + a1 a2 -a3 7- Dihexagonal bipyramid (21-31) + + + + + ++ + + + + +
  123. 123. Compound form Hexagonal prism (m = 6) Hexagonal bipyramid (m = 12)
  124. 124. Trigonal system Ɣ β α a1 a2 -a3 c / ca3a2a1 90βα 120Ɣ ditrigonal scalenohedron Class
  125. 125. 31 Trigonal system 1-Axis of symmetry 2- Center of symmetry
  126. 126. Trigonal system 3- Plane of symmetry 3 vertical plane
  127. 127. ______ 32 m n3 Trigonal system Complete Symmetrical Formula
  128. 128. a1 a2 (E)(W) Stereographic Projection of Symmetry elements of the Triagonal System -a3
  129. 129. Forms Basal Pinacoid First Order Prism Second Order Prism Dihexagonal prism Second Order bipyramid Trigonal rhombohedron Ditrigonal scalenohedron
  130. 130. Positive trigonal rhombohedron [h0hl] - h0hl - a1 -a3 a2 Trigonal system Crystal form a1 -a3 a2 Positive rhombohedron {10-11} + ++ a1 a2 + + + + + + Stereographic Projection
  131. 131. Negative trigonal rhombohedron [0kkl] - 0kkl - a1 -a 3 a2 Trigonal system a1 -a3 a2 a1 -a3 a2 Positive rhombohedron {10-11} Negative rhombohedron {01-11} + ++ + + + a1 -a3 a2 a1 a2 + + + + + + + + + + + + Stereographic Projection
  132. 132. Positive ditrigonal scalenohedron [hkwl] - hkwl - a1 -a3 a2 Trigonal system Stereographic projection of the Tr a1 -a3 Positive rhombohedron {10-11} + a1 -a3 a2 Positive Scalenohedron {21-31} + + + + + + Stereographic Projection
  133. 133. Negative ditrigonal scalenohedron [hkwl] - hkwl - a1 -a3 a2 Trigonal system Stereographic projection of the Triagonal System Forms. a1 -a3 a1 -a3 Positive rhombohedron {10-11} Negative rhombohedron {01-11} + + a1 -a3 a2 a1 -a3 a2 Negative Scalenohedron {12-31}Positive Scalenohedron {21-31} + + + + + + + + + + + + Stereographic Projection
  134. 134. Monoclinic system 90Ɣα cba / / β 90/ c a b β Ɣ α Class
  135. 135. 1 Monoclinic system 1-Axis of symmetry 2- Center of symmetry
  136. 136. Monoclinic system 3- Plane of symmetry 1 vertical plane
  137. 137. 2______ m n Monoclinic system Complete Symmetrical Formula
  138. 138. Stereographic Projection of Symmetry elements of the Monoclinic System a b (E)(W)
  139. 139. Monoclinic front pinacoid [100] Monoclinic side pinacoid [010] Monoclinic basal pinacoid [001] Monoclinic system Stereographic Projection • pinacoid Crystal form 1- Basal Pinacoida +(001) 2- Side Pinacoida ++ + (00-1) Stereographic projection of the Monoclinic System Forms. 1- Basal Pinacoida +(001) 2- Side Pinacoida ++ 3- Front pinacoid a + + (00-1)
  140. 140. Monoclinic prism [hk0] Monoclinic system Stereographic Projection m {hk0} or {110} 4- Monoclinic Prism a + ++ + ++ (-111)
  141. 141. Positive hemibipyramid [hkl] Monoclinic system Positive Hemibipyramid {hkl} or {111} Negative Hemibipyramid {-hkl} or {-111} hkl 7- Hemibipyramid Front View Back View {111} {-111} • hemibipyramid Negative hemibipyramid [hkl] - 54- Monoclinic Prism a ++ a a + Positive (101) 7-Hemibipyramid a a ++ (111) ++ (-111) Stereographic Projection 4- M a ++ 7 a ++ (-111) NegativePositive
  142. 142. 5- Side Dome (a-dome)4- Monoclinic Prism a + + a ++ a a + (101) +(-101) ++ (111) + (-111) - 011 Monoclinic system • Dome - hemi-orthodome Positive hemi-orthodome [h0l] Negative hemi-orthodome [h0l] - side dome [0kl] - 101 011 side dome [0kl]Positive hemidome [h0l] 5- Side Dome (a-dome)4- Monoclinic Prism a a 6- Hemi-orthodome a a + Positive (101) + Negative (-101) 7-Hemibipyramid a a ++ (111) ++ (-111) hemi-orthodome Stereographic Projection
  143. 143. Triclinic system cba / / c a b β Ɣ α /α β Ɣ 90// Class Pinacoid
  144. 144. Triclinic system 1-Axis of symmetry = - 2- Center of symmetry = n 3- Plane of symmetry = -
  145. 145. n Triclinic system Complete Symmetrical Formula
  146. 146. Stereographic Projection of Symmetry elements of the Triclinic System
  147. 147. front pinacoid [100] side pinacoid [010] basal pinacoid [001] Triclinic system Crystal form Stereographic projection of theTriclinic System Forms. 1- Basal Pinacoida a a 2- Side Pinacoid 3- Frontl Pinacoid + + + + + Stereographic projection of theTriclinic System Forms. 1- Basal Pinacoida a a 2- Side Pinacoid 3- Frontl Pinacoid + + + + + Stereographic Projection
  148. 148. Right hemi-prism [hk0] Left hemi-prism [hk0] Triclinic system - a a a a a a a a a a + + + + + + + + + 5- Hemi-b-dome {h0l}: two forms {101} and {-101} 4- Hemi-a- dome { 0kl} : two forms {011} and {0-11} 6- Hemi-prism{hk0} and {h-k0} Upper left quarter bipyramid Upper right quarter bipyramid Lower left quarter bipyramid Lower right quarter bipyramid
  149. 149. Hemi-brachydome(0kl) Hemi-macrodome(h0l) Triclinic system a a a a + + + + 5- Hemi-b-dome {h0l}: two forms {101} and {-101} 4- Hemi-a- dome { 0kl} : two forms {011} and {0-11}
  150. 150. Upper right quarter bipyramid [hkl] Upper left quarter bipyramid [hkl] Lower right quarter bipyramid [hkl] Lower left quarter bipyramid [hkl] - - -- Triclinic system a a a a a a + + + + + + 4- Hemi-a- dome { 0kl} : two forms {011} and {0-11} Upper left quarter bipyramid Upper right quarter bipyramid Lower left quarter bipyramid Lower right quarter bipyramid
  151. 151. Crystal Morphology • The angular relationships, size and shape of faces on a crystal • Bravais Law – crystal faces will most commonly occur on lattice planes with the highest density of atoms Planes AB and AC will be the most common crystal faces in this cubic lattice array
  152. 152. Unit Cell Types in Bravais Lattices P – Primitive; nodes at corners only C – Side-centered; nodes at corners and in center of one set of faces (usually C) F – Face-centered; nodes at corners and in center of all faces I – Body-centered; nodes at corners and in center of cell

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