7/28/2019 3 Crystal

1/50

CRYSTALLOGRAPHYINTRUDUCTION: Mineralogy is the branch of science dealing with the study of

minerals. Nowdays a mineral is defined as A geological body, occurring in the

inorganic mature and possesses a certain characteristic atomic structure which is

expressed in its crystalline form, physical properties and chemical homogeneity. In our course of Mineralogy and Crystallography we are going to deal with the

internal atomic structure of minerals which is closely related to the study of

their external form of their crystals (Crystallography), their physical properties

( Chemical Mineralogy) and their optical properties (optical Mineralogy). Formation of crystal : A crystal is a solid body bounded by plane. Natural

surfaces (crystal faces), which are the external expression of a regular internal

arrangement of constituent atoms or ions. The study of the arrangement of atoms within a crystal, that is, of atomic

structure, has been made in recent years by x-ray analysis. The smallest complete unit of the three dimensional pattern- which is repeated

through the crystal- is called the unit cell.

The whole pattern or from of the external crystal form is formed by stacking unit cellstogether. To take a simple example, in crystals of sodium chloride (Halite) the atoms

of Na and Cl are arranged at the corners of a series of cubes, as shown in(Fig. 1).

7/28/2019 3 Crystal

2/50

The unit cell of sodium chloride contains four atoms of Na and four of Cl,

whose arrangement is exactly similar to that in every other unit cell of the

substance.

It is to be noted that the number of atoms in the unit cell of a particular

minerals is not necessarily the same as in its formula, but is usually some

simple multiple; for NaCl; this multiple is four. Space Lattice: Naturally the atoms of the different elements that enter in the

composition of a mineral or its crystal are arranged together in a regular three

dimensional pattern containing their unit cells in an arrangement called "space

lattice". The space lattice formed by points in space. Each lattice point represents the

center of gravity of an ion, atom or molecule which occupies a similar

surrounding.

linear pattern

two dimensional pattern

Three

dimensional pattern

7/28/2019 3 Crystal

3/50

The 14 Three-Dimensional Bravais Lattices

1. Primitive Triclinic

7/28/2019 3 Crystal

4/50

C-centered are no constraints on axial lengths or onb. The standard choice of axes isthat b is unique. The centered cell is also unique and preserves the axis identities andhas an additional lattice point at 1/2+x, 1/2+y, z, so that there is an additional lattice point per cell for a total of two, whereas the primitive cell have just one lattice point per cell (eight corners, each of which is 1/8th within the cell). Because there areseveral possible choices of the a and b axes, it is possible to choose an A- centered or I-centered cell. It is possible to show that centering of any other face reduces to one of these two.

7/28/2019 3 Crystal

5/50

4. & 5. Primitive C-centered Primitive and C-centered orthorhombic. alpha = betagamma = 90. There are no constraints on axial lengths. Labeling of axes is arbitrary.Just as in the monoclinic case, the centered cell preserves the axis orthogonality andhas an additional lattice point at 1/2+x, 1/2+y, z. It would also be possible to chooseequivalent A or B centered cell, but conventionallyc is the centered axis.

7/28/2019 3 Crystal

6/50

6 & 7. I-centered F-centered centered (body-centered) cell has an additional lattice point at 1/2+x, 1/2+y, 1/2+z, for a total of two points per cell. In the F-centered celleach of the faces contains 1/2 of an additional lattice point for a total of four per cell.In each, the labeling of axes is arbitrary.

7/28/2019 3 Crystal

7/50

8 & 9. Primitive I-centered Primitive and I-centered Tetragonal alpha = beta = gamma= 90 degrees.a = b; and c is unique axis with 4 or -4 symmetry. The I- centered(body-centered) cell has an additional lattice point at 1/2+x, 1/2+y, 1/2+z, for a totalof two points per cell. Note that there is no C-centered tetragonal cell be cause itwould be possible to choose a primitive tetragonal cell with half the volume. Similarlyan F-centered cell would reduce to an I-centered cell.

10 & 11. Primitive I-centered Primitive and I-centered Cubic (Isometric) alpha = beta= gamma = 90 a = b = c. These are similar to the above except for the additionalaxial length constraint.

12. F-centered Face Centered Cubic (Isometric) alpha = beta = gamma = 90a = b =c. Each of the six faces contains a lattice point for a total of four per cell.

13. 120 120 Primitive R-centered Primitive Hexagonal

The R-centered cell contains lattice points at 1/3 and 2/3 along the body diagonal.This makes it pos sible to choose an alternative primitive cell such that alpha = beta =gamma, but not 90 or 120 degrees.

7/28/2019 3 Crystal

8/50

CRYSTAL SYMMETRY: (External elements of symmetry)

The fundamental symmetry operations are: (1) rotation about an axis (2)

reflection across a plane (3) rotation about an axis combined with inversion (rotary

inversion). (4) Inversion about a center alone is considered as 1- fold axis of rotary

inversion.

(1) Rotation axis: The rotation axis is an imaginary line through a crystal about

which the crystal about which the crystal may be rotated and repeat itself-in

appearance two or more times during

a complete rotation. The nature of crystals is

such that no symmetry axes other than

1-, 2-, 3-, 4-, and 6- fold can exist (fig. 3).

Axis of Rotation = imaginary line through a crystal about which the crystal may be

rotated and repeat itself in appearance (1,2,3,4 or 6 times during a complete rotation).

Permissible rotations - Proper

1-fold 360 I Identity

2-fold 180 2

3-fold 120 3

4-fold 90 4

6-fold 60 6

7/28/2019 3 Crystal

9/50

(2) Mirror plane : A mirror or symmetry plane is an imaginary plane that divides a

crystal into halves, each of which, in a perfectly developed crystal, is the mirror image

of the other (fig. 4).

Mirror Plane = imaginary plane that divides a crystal into halves, each of which is

the mirror image of the other.

(3) Inversion axis: this composite symmetry element combines a rotation about an

axis with inversion through the center (Fig. 5).

(4) Center of symmetry : A crystal is said to have a center of symmetry if an

imaginary line can be passed from any point on its surface through its center and a

similar point is found on the line at an equal distance beyond the center (fig. 6).

Fig. 5: Inversion axis Fig. 6: Center of symmetry

Symmetry notation : The rotation axes are represented by the numbers 2,3, 4,

and 6 according to whether they are diad, triad, tetrad, and hexad

axes while the corresponding inversion axes have they symbols2'.., 3', 4'

and 6' respectively. On the other hand the mir ror plane is referred to by

latter m and the center of symmetry by 1'.

7/28/2019 3 Crystal

10/50

Crystal notation : crystallographic axes: they are certain lines passing through

the center of the ideal crystal as axes of reference. These imaginary lines are

called the crystallographic axes and are taken parallel to the intersection edges

of major crystal faces. All crystals, with the exception of these belonging to

the hexagonal and trigonal systems are referred to three crystallographic axes

(fig. 7).

Crystallographic Axes

CRYSTAL SYSTEMS: on the basis of the symmetry elements, crystals aregrouped into seven major divisions, the seven crystal systems.

Crystalsystem

crystallographicaxes

Rotation axes Planessymmetry

Ex.

Cubic a = b = c = = = 90

Four triad axes/ Four 3-fold :

3- , 4 6

9-planes :

\6

Pyrite, Halite,Galena,

Garnet,Diamond,Fluorite,Ag,Cu , crumite

Tetragonal

a = b # c = = = 90

5 - : ,

5-

Wulfenite,Rutile, Zircon,Chalcopyrite

Hexagonal

a1 = a2 = a3 # c1 = 2 = 3 =120, = 90

1-

6

7 :1- : 6-

Quartz, Beryl(Emerald),Apatite,Corundum(Ruby,Sapphire

7/28/2019 3 Crystal

11/50

Trigonal a1 = a2 = a3 # c

1 = 2 = 3 =120, = 90

Calcite,hematite,dolomite

Orthorhombic a # b # c = = = 90

Sulfur, Barite,Olivine, Topaz

Monoclinic

a # b # c = = 90, # 90

Orthoclase,Malachite,Azurite, Mica,

Gypsum, Talc

Triclinic

a # b # c # # # 90

-No rotationaxes.

Turquoise,Kyanite,Albite,Plagioclase

Crystal Morphology

A face is designated by Miller indices in parentheses, e.g. (100) (111) etc. A form is a face plus its symmetric equivalents(in curly brackets) e.g {100}, {111}.

A direction in crystal space is given in square brackets e.g. [100], Form: the form consist of a group of crystal faces all of which have the same

relation to the elements of symmetry. And display the same chemical and

physical properties because all are underline by the same atoms in the same

geometrical arrangement.

e.g form a is of 4 facies in(fig. 9) and of 6 facies in (fig. 10), form C is of 2 facies

form P of 8 facies, etc.

so that in (fig. 9): a-----4, P-----8, C-----2.

in (fig.10): a-----6, e-----12.

7/28/2019 3 Crystal

12/50

In each crystal classes there is form the faces of which intersects each of the

crystallographic axes at different lengths; this is general form, {hkl }. At other forms

that may be present are special forms.

A crystal form is a crystal face plus its symmetric equivalents. For example, a cube isa crystal form made up of six symmetrically equivalent faces.

A special form is a crystal form that is repeated by the symmetry operations ontoitself so that there are fewer faces than the order of the point group. The projections of special forms or special faces will lie on symmetry operations in our stereographic projections.

A general form is one that is not repeated onto itself by the symmetry operations sothat it has the same number of faces as the order of the group.

Forms are either general or special. In our stereographic projections, we will plot onlythe general form because this defines the point group. In addition to being special or general, forms may also be open or closed.

A closed form is one that encloses a volume; (e.g., a cube, tetrahedron, octahedron,etc). A closed form may then be the only form present on a perfect crystal.

An open form is one that does not enclose a volume; (e.g., prism, pinacoid, etc.). Acrystal that has an open form must have more than one form present.

Each form of the cubic system has a special name, but the same general names are

used for the forms of the other systems; the following examples are very common:

Pinacoid Prism Pyramids

7/28/2019 3 Crystal

13/50

Scalenohedron Trapezohedrn Pedion Bipyramids / Dipyramid

Dome or Sphenoid Rhombohedron

PARAMETERS AND INDICES: crystal faces are defined by indicating

their intercepts on the crystallographic axes (whether its parallel to two axes

and intersects the third, or is parallel to one axis and intersects the other two,

or inter sects all three). In addition one must determine at what relative

distance the face intersects the different axes. The parameters are 1a, 1b, 1c or

1a. 1b, 2c or 1a, 1b, c. The indices of the face (the miller indices) are a series of whole numbers

which have been derived from the parameters by their inversion and, if

necessary, the subsequent clearing of fractions. The indices of a face are

always given as three numbers refer to a, b, c or as four numbers refer to a1,

a2, a3, and c.

7/28/2019 3 Crystal

14/50

Examples:

parameters indices

1a, 1b, c (110)

1a, 1b, 2c (22'1)1a, 1b, c (112)

1a1 = 1a2 = 2a3 , c (2210)

Miller Indices

X=Y=Z=

Halite CubeMiller Indices Plane cuts axes at intercepts ( ,3,2).

7/28/2019 3 Crystal

15/50

To get Miller indices, invert and clear fractions. (1/ , 1/3, 1/2) (x6)= (0, 2, 3) General face is ( h,k,l )Miller Indices The cube face is (100) The cube form {100} is comprises faces (100), (010), (001), (100), (0-10), (00-1)

Stereographic Projections.

There are three common methods to graphically display orientations of vectors inthree dimen sions. In order to describe faces of crystals we would like to plot thevectors normal (perpendicular) to crystal faces.

1. Spherical. The simplest to visualize is the spherical projection. In this method, thevector is merely projected vertically onto the equatorial plane of the sphere. However,this method has the serious disadvantage of compressing the low-angle vectors ontothe outside of the plot.

2. Stereographic. This disadvantage can be avoided if, instead of projecting

vertically, one projectsradially to the pole of theopposite hemisphere. This is the

standard stereographic or equal-area plot that we will use to plot poles

(perpendiculars) to faces of crystals. The plot is also sometimes called the "Wulff

net". If the angle made by a vector with the vertical is r, then the distance from thecenter of the plot is R tan r/2, where R is the radius.

3. Gnomonic. There is also a third type of plot called the gnomonic projection inwhich the vector is extended till it intersects a plane tangent to the sphere at the north pole. This has the disadvantage of not being able to display horizontal vectors. It is,however, what arises naturally from x-ray and electron diffraction experiments whereeach node corresponds to a lattice plane in real space and results in areciprocallattice.

7/28/2019 3 Crystal

16/50

However, for our purposes of displaying the orientations of crystal faces we will usethe stereo graphic projection exclusively.

We will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents (generalformhkl ).

Illustrated above are the s tereographic projections for Triclinic point groups 1 and -1.

CUBIC SYSTEMCrystallographic Axes: Three axes of equal length that make right angles with

each other.

a = b = c = = = 90

IsometricSystem

90 9090

ISOMETRIC

= = = 90

a = b = c

c = a

b = aa

Pyrite, Galena,Halite, Fluorite,

Garnet, Diamond

Unique Symmetry:Four 3-fold axes

Symmetry:

Galena Type

7/28/2019 3 Crystal

17/50

13 rotation axes + 9 mirror planes

3 tetrad crystallographic axes

4 triad diagonal axes

6 diad diagonal axes

Forms:

Six square faces (cube), {001}

8 equilateral triangular faces (octahedron), {111}

12 rhombshaped faces (dodecahedron), {011}

24 isosceles triangular faces (tetrahexahedron), {0kl}

24 trapezium rhombshaped faces (trapezohedron), {hhl}

24 isosceles triangular faces (trioctahedron), {hll}

48 triangular faces (octahexahedron), {hkl}

Forms of Cubic System

Combination of Cubic Forms:

Cube & dodecahedron

Cube & octahedron

Cube, octahedron & dodecahedron

7/28/2019 3 Crystal

18/50

Dodecahedron& octahedron

Octahedron & dodecahedron

Mineral Examples:

Halite, Fluorite, Galena, Diamond, Magnetite, pyrite and gold

TETRAGONAL SYSTEM Crystallographic Axes: Three axes of that make right angles with each other;

two equal horizontal axes (a, b) with different length

vertical axis (c).

TetragonalSystem

90 9090

TETRAGONAL= = = 90

a = b cc a

b = aa

Wulfenite, Zircon,

Chalcopyrite, Rutile

Unique Symmetry:One 4-fold axis

Symmetry:

Zircon Type

a = b # c = = =

90

7/28/2019 3 Crystal

19/50

One tetrad, 4 diad crystallographic axes and 5 mirror planes (4 vertical + 1

horizontal).

Forms:4 faces, first order tetragonal prism, {100}

4 faces, second order tetragonal prism, {010}8 faces, ditetragonal prism, {hk0}

8 faces, first order tetragonal dipyramid {hhl}

8 faces, second order tetragonal dipyramid {0kl}

16 faces, ditetragonal dipyramid {hkl}

Combination of Tetragonal Forms:~ tetragonal prism & ~ tetragonal dipyramid

7/28/2019 3 Crystal

20/50

Mineral Examples:Zircon, Cassiterite, ..etc.

HEXAGONAL SYSTEMCrystallographic Axes:

a1 = a2 = a3 # c 1 = 2 = 3 = 120 ,

= 90

7/28/2019 3 Crystal

21/50

HexagonalSystem

12090 90

H E X A G O N A L

=

,

= =

a = c

c > a

Q u a r t z ,

B e r y

l ( E m e r a

l d ) ,

A p a

t i t e

, G r a p

h i t e

,

C o r u m

d u m

( R u

b y ,

S a p p

h i r e

)

b = a

U n

i q u e

S y m m e

t r y :

O n e

6 - f

o l d a x

i s

a

Symmetry:Beryl Type

one vertical hexad, 6 horizontal diad crystallographic axes and 7 mirror planes.

Forms:

6 faces, first order hexagonal prism, {101-0}

6 faces, second order hexagonal prism, {112-0}12 faces, dihexagonal prism, {hk1-0}

7/28/2019 3 Crystal

22/50

12 faces, first order hexagonal dipyramid {h0h -l}

12 faces, second order hexagonal dipyramid {hh(2-h)l}

24 faces, dihexagonal dipyramid {hk1-l}

Combination of Hexagonal Forms:

e.g. Beryl

~ hexagonal prism & ~ hexagonal dipyramid

Mineral Examples:

beryl, molybdenite, pyrrotite , ..etc.

TRIGONAL SYSTEM

Crystallographic Axes:

a1 = a2 = a3 # c 1 = 2 = 3 = 120 , =

90

7/28/2019 3 Crystal

23/50

Symmetry:

Calcite Type

One vertical triad, 3 horizontal diad crystallographic axes and 3 mirror planes

(vertical).

Forms:

(1) Rhombohedron:

6 rhomb-shaped faces, (cube deformed)

Positive rhombohedron, {h0h-l} & Negative rhombohedron {0hh-l}

(2) Scalenohedron:

12 Scalene triangular faces of a di-hexagonal dipyramid.

The characteristics of the Scalenohedron are the zigzag appearance of the

middle edges which differentials it from the dipyramid, and the alternately

more and less obtuse angles over the edges that meet at the vertices of the

form.

Positive Scalenohedron, {hk1-l} & Negative Scalenohedron {kh1-l}

7/28/2019 3 Crystal

24/50

Combination of Trigonal Forms:

Mineral Examples:

Calcite, dolomite, magnezite, ..etc.

7/28/2019 3 Crystal

25/50

ORTHOROMBIC SYSTEMCrystallographic Axes:

Symmetry:

Barytes Type

3 crystallographic axes diad perpendicular to each other and 3 mirror planes

perpendicular to each other.

Forms:

Front Orthorhombic Pinacoid {100}

Side Orthorhombic Pinacoid {010}

Basal Orthorhombic Pinacoid {001}

a # b # c = = = 90

OrthorhombicSystem

90 9090

ORTHORHOMBIC

= = = 90

a b cc a b aa

Sulfur, Barite,

Olivine, Topaz

Unique Symmetry:

Three 2-fold axes

7/28/2019 3 Crystal

26/50

4 faces, first order Orthorhombic prism or side dome {0kl}

4 faces, second order Orthorhombic prism or front dome {h0l}

4 faces, third order Orthorhombic prism or vertical Orthorhombic prism {hk0}

5.4a Prism {110} and pinacoid {001}

5.4b Prism {101} and pinacoid {010}

5.4c Rhombic prism {011}and pinacoid {100}

8 faces Orthorhombic dipyramid {hkl}

5.6a Rhombic dipyramid5.6b 5.6c Sulfur crystal

Combination of Orthorhombic Forms:

~ Orthorhombic prism , ~ Orthorhombic dipyramid &Orthorhombic Pinacoid

Mineral Examples:

sulfur, staurolite, barite, ..etc.

7/28/2019 3 Crystal

27/50

MONCLINIC SYSTEMCrystallographic Axes:

a # b # c

Angle between a, b named and

Angle between b, c named = 90

Hence = = 90

Angle between a, c named = >

90 (oblique angle)

MonoclinicSystem

90 90

MONOCLINIC

= = 90 , 90

a b cc a b aa

O r t h o

c l a s e ,

M a l a c h i t e

, A z u r i t e ,

G y p s u m

, M i c

a , T

a l c

Unique Symmetry:One 2-fold axis

90

Symmetry:

Gypsum Type

The b axis is rotation diad and a-c

plane is mirror plane.

7/28/2019 3 Crystal

28/50

Forms:

Front Monoclinic Pinacoid {100}

Side Monoclinic Pinacoid {010}

Basal Monoclinic Pinacoid {001}

4 faces, first order Monoclinic prism or side dome

{0kl}

4 faces, second order Monoclinic

prism or front dome {h0l}

4 faces, third order Monoclinic prism

or vertical Monoclinic prism {hk0}

4 faces, fours order Monoclinic prism or Hemi-pyramid {hkl}

Combination of Monoclinic Forms:~ Monoclinic prism, ~ Monoclinic dipyramid & Monoclinic Pinacoid

NOTE : F igures a, b, and c are common forms for the mineral

orthoclase and d i s a common form for seleni te (gypsum)

]

Mineral Examples:

gypsum, pyroxene, amphibole, orthoclase. ..etc.

7/28/2019 3 Crystal

29/50

TRICLINIC SYSTEMCrystallographic Axes:

a # b # c

# # # 90

TriclinicSystem

9 0

90

TRICLINIC

90

a b c

c a

T u r q u o

i s e , P l a

g i o c l a s e

K y a n i t e

, A l b i t e

Unique Symmetry:None

9 0

b a

a

Symmetry:

Axinite Type

7/28/2019 3 Crystal

30/50

one noonad axis of rotation or inversion which is

equivalent to a symmetry center , no axes of

symmetry and no planes of symmetry

Forms:

Front Triclinic Pinacoid {100}

Side Triclinic Pinacoid {010}

Basal Triclinic Pinacoid {001}

2 faces, first order Triclinic prism or side dome {0kl}

2 faces, second order Triclinic prism or front dome {h0l}

2 faces, third order Triclinic prism or vertical Monoclinic prism {hk0}

2 faces, fours order Triclinic prism or Hemi-pyramid {hkl}

Figure 8.3 Triclinic pinacoids, or parallelohedrons

Combination of Triclinic Forms:

~ Triclinic prism, ~ Triclinic dipyramid & Triclinic Pinacoid

Mineral Examples:

plagioclase (feldspars), wallastonite, ..etc.

7/28/2019 3 Crystal

31/50

Crystal Systems

System Axes Angles Unique Symmetry Diagram Examples

Isometric

Tetragonal

Hexagonal

Orthorhombic

Monoclinic

Triclinic

7/28/2019 3 Crystal

32/50

MINERALOGYTechniques of mineral identifications

I- Physical Properties in hand specimens (Physical Mineralogy)

II-

Optical Properties in petrographic microscope (Optical Mineralogy)III- Chemical properties (chemistry of minerals and blowpipe test)

IV- Internal structure of crystal of the minerals (x- ray techniques)

I-PHYSICAL PROPERTIES / MINERALOGYThe Physical Properties are very important in the identification of

minerals e.g. 1- Cleavage 2- Parting 3- Fracture 4- Tenacity 5- Specific Gravity

6- Luster 7- Colour 8- Streak 9- Tarnish 10- Magnetism 11- Hardness.

1- Cleavage:It a mineral, when the proper force is applied, break so that it yields

definite plane surfaces, it is said to possess a cleavage (perfect 1 set or 2

sets.etc or imperfect or lacking ..). Cleavage is dependent on the

crystal structure and takes place only parallel to atomic planes which

have weak binding force between them.

2- Parting:

Twin crystals, especially polysynthetic twins, may separate easily alongthe composition planes. When plane surfaces are produced on a mineral

by its breaking along some such predetermined plane, it is said to have a

parting.

3- Fracture:By the fracture of a mineral is meant the way in which it breaks, when it

does not yield along cleavage or parting surfaces (Conchoidal, Fibrous,

Hackly, Uneven or Irregular). 4- Tenacity:

(Cohesiveness): it is the resistance that a mineral offers to breaking,

crushing, bendin or tearing: Brittle, Malleable, Sactile, Flexible, and

Elastic.

7/28/2019 3 Crystal

33/50

5- Specific Gravity:Specific Gravity or relative density of a mineral is a number that

expresses the ratio between its weight and the weight of an equal volume

of water at 4c. The Specific Gravity of a crystalline substance isdependent on:

A- The kind of atoms of which it is composed (atomic wt.).

B- The number in which the atoms are packed together. (Heavy, Moderate,Light).

6- Luster:The general appearance of the surface of a mineral in reflected light is

called Luster: Metallic, Sub- Metallic, Non- Metallic (Vitreous, Pearly,Silky, Greasy, and Adamantine).

7- Colour:The colour of minerals id one of their most important physical properties

especially those of metallic luster e.g. brass yellow of chalcopyrite. The

change of colour in a mineral is often due to change in composition or to

the presence of impurities.

8- streak:The colour of the fine powder of a mineral is known as its streak which is

the usually constant for a mineral. 9- Tarnish:

A mineral is said to show a tarnish when the colour of the surface differs

from that of the interior. e.g. in copper minerals (chalcocite, bornite and

chalcopyrite).

10- Magnetism:The power to attract as possessed by a magnet.

or those minerals that, in their natural state, will be attracted to an iron

magnet are said to be magnetic.

In the magnetic field of a powerful electromagnet many other minerals

containing iron, are drown to the magnet. Because of this, the

electromagnet is an important means of separating mixtures of mineral

7/28/2019 3 Crystal

34/50

grains having different magnetic susceptibilities. (Ex. Magnetite, and less

degree pyrrhotite).

11- Hardness:

(The quality or state of being hard).The resistance that smooth surface of a mineral offers to scratching is its

hardness.

Hardness like the other physical properties depends on the atomic

structure of the mineral and the difference of binding forces

between the atoms.

Scale of Hardiness

Hardness

1. Talc

2. Gypsum

3. Calcite

4. Fluorite

5. Apatite

6. Orthoclase

7. Quartz

8. Topaz

9. Corundum

10. Diamond

II- OPTICAL MINERALOGYThe branch of mineralogy, which studies minerals under Polarizing

Microscope.

III- CHEMICAL MINERALOGY(Chemistry of minerals)

"The study of the relationships between chemical composition, internal

atomic structure and physical properties of the mineral"

7/28/2019 3 Crystal

35/50

Atomic Structure of the minerals:Minerals are compound of their constituent elements, while rocks are

mixture of their component minerals. Thus the Quartz is a compound (Silica) of

the elements silicon and oxygen.The proportion of constituent elements of a mineral is represented by a

chemical formula; thus Calcite is composed of calcium, carbon and oxygen in the

proportion of 1:1:3 respectively. The chemical formula can be easily calculated

from chemical analysis of its mineral.

Atomic bonding: there are fore main ways in which may join together:1-

ionic bond (NaCl) 2- covalent bond (Diamond; C) 3- metallic bond (metals)4-

Van der Waals or residual bond( associated with other bonds e.g. Graphite).

More than one type of bond may occur in a single compound (mineral). In

graphite fore example, the carbon atoms are linked in sheets by covalent bond

and the sheets are linked together by Van der Waals bonds.

Coordination:In ionic crystals each positive ion (cation) is surrounded by a number of

negative ions (anions), at a distance fixed by the sum of their radii. The number

of anions that can fit around each cation is known as the Coordination numberof cation and termed Kz. The number can be determined by the ratio of the

radius of the cation to that of the anion which expressed by radius ratio. The

different types of Kz are shown in the (Fig .).RR = radius of cation/radius of anion (usually oxygen)

Radius Ratio (RR)

7/28/2019 3 Crystal

36/50

isomorphism:Isomorphous replacement of cations by others of similar size and equal

charge is common in silicates. Thus, Fe2+

readily replaces Mg2+

, the two ionshaving nearly the same size, and Fe3+ replaces Al. such replacement is

rondom and results in the minerals concerned variable compositions. The

possibility of isomorphous substitution depends more upon ionic size than

upon valancy. This is well shown by the fact that Na+ is commonly replaced

by Ca2+ *as in the plagioclase feldspare), but less readily by K + . this is due to

that the Na and Ca ions have almost the same dimensions, whereas the K-

ions is considerably larger than Na. Anions of similar size such as O2-, OH-, F-

can also be substituted for one another.

When Si is replaced by Al in 4-fold coordination in silicates, addifference

in ionic charge is involved, since an ion with a lower charge (3+) is substituted

for one with a higher (4+). To make the structure electrically neutral another

cation must be added, so that the sum of the positive charges equals that of

the negative. This isomorphous substitution between elements of different

valency is, therefore, termed coupled atomic substitution.

The plagioclase for example;

Al + Ca replace Si + Na

3 + 2 4 + 1

In which sum of the valence equal 5. this coupled atomic substitution

gives transitional members between the Ca-feldspar (Anorthite) and the Na-

feldspar (albite).

The simplest cases of isomorphous substitution occur when the ions are

equal both in charge and in size, e.g. Mg2+ and Fe2+ as in olivine in which

forsterite ( Mg3SiO4) and fayalite (Fe2 SiO4) are isomorphous. The two

atoms or ions occurring in a mineral are called diadochic if they are capable

of replacing each other in the structure of one mineral and not in another;

each occupying the others position, as in case of Mg2+ and Fe2+ ions in the

olivine structure.

There is usually a limit to the exact to which isomorphous substitution

takes place . the higher temperature of crystallization, gives greater chance of

7/28/2019 3 Crystal

37/50

isomorphus substitution. Increasing rate of crystal growth increases the

chance of isomorphism. solid solution and exsolution:

we have observed that most minerals are variable in their composition.Substitution of one element by another is very common. Any ion in the

structure may be replaced by another ion of similar radius without casing

serious distortion of the structure. When crystals of two components contain

any proportion of the two substance and have unite cell dimensions

intermediate between those of pure components, such crystals are called

mixed crystals or crystalline solid solutions. A solid solution (or mixed

crystal) an be simply defined as a homogeneous crystalline solid of variable

composition. It was early found that many isomorphus substances have the

property of forming solid solution.

Now it is found that many isomorphus substances show little or or no

solid solution (e.g. calcite, CaCo3 and smithsonite, Zn Co3) and extensive

solid solution may occur between substances that are not isomorphus (e.g.

pyrite, FeS and sphalerite, ZnS). On this accunt it must be emphasized that

isomorphism is neither necessary to nor sufficient for solid solution

formation. Isomorphism and solid solution are distinct concepts and should

not be confused.

Since atomic substitution is generally greater at higher temperatures, it

follows that a solid solution formed at high temperature and no longer be

stable at lower temperatures. A solid solution in which two different

elements, A and B are completely inter replaceable at high temperatures but

lower temperatures will tend to break down on cooling into two separate

phases, on rich in A and the other rich in B. this break down of a

homogeneous solid solution id known as exsolution. For example, in the alkali

feldspars K and Na are completely interchangeable at high temperatures; for

any composition in the system KAlSi3O8 - NaAl Si3O8 there is a single

phase solid solution (K, Na)Al Si3O8, which show intermediate unit cell

dimensions Physical Properties. At ordinary temperature the degree of

natural replacement of K and Na in feldspar is quite small, solid solutions of

intermediate composition in this system generally break down, on cooling,

7/28/2019 3 Crystal

38/50

into an intergrowth of Na-rich feldspar and K- rich feldspar known as

perthite.

defect lattice structures:The other type of solid solutions is that associated with defect lattices, in

which some of the atoms are missing leaving vacant lattice position. A good

ezample is the mineral pyrrhotite, whose analyses always show more

sulphure than corresponds to the formula FeS. This was, for a long time,

described as solid solution of sulphure in FeS. Actually the excess of sulphure

shown by analyses is the lattice; there is a defectably of Fe not an excess of S.

pseudomorphism:Pseudomorphism is the phenomenon of alteration or metasomatic

replacement of crystal of a mineral by other mineral without change of

external form of the original crystal. The new crystal is called pseudomorph

or fals form. Pseudomorphism may be formed in one of the following ways:

a) Paramorphism: in which no change in chemical composition has takenplace e.g. transformation of aragonite (CaCO3, orthorhombic) to calcite (also

CaCO3, trigonal) and rutile to brookite.b) Substitution: in which there is a gradual removal of the original materialand a responding and simultaneous replacement of two by another with no

chemical reaction between the two, e.g. formation of quartz SiO2 after

fluorite CaF2 and also silica after the wood fibers to petrified wood.

c) Alteration: in which the new mineral has been formed from the originalmineral by a process of chemical alteration may originate by:

1. The loss of a constituent (e.g. change of magnetite, Fe3O4 to hematite,Fe2O3 by loss of Fe).

2. The gain (addition) of a constituent (e.g. change of anhydrite, CaSO4

to gypsum, CaSO4.2H2O by addition of H2O) and malachite after

cuprite.

3. A partial exchange of constituents (e.g. goethite, HFeO3 after pyrite,

FeS2 by loss of S and addition of H2O

polymorphism:

7/28/2019 3 Crystal

39/50

An element or compound that can exist in more than one crystal form is

said to be isomorphus, each form has different physical properties and a

distinct crystal structure.

The new form of the same chemical composition is formed as a result of

changes in temperatures, pressure and chemical environment.

A polymorphism substance may be described as dimorphic/trimorphic

are depending to the number of distinct crystalline forms the substance is an

element, the polymorphism is termed allotropy, e.g. carbon which occurs as

graphite ( hexagonal) and diamond (cubic).

Two types of polymorphism are recognized, according whether the

change from one polymorph to another is reversible and takes place at a

definite temperature and pressure; is known as anantiotropy, or is

irreversible and does not take place at a definite temperature and pressure

and termed monotropy.

Examples of anantiotropic polymorphism

Quartz

(SiO2)870C

Tridymite

(SiO2)1470C

Cristobalite

(SiO2)

Triagonal Hexagonal Cubic

Brookite(TiO2)

900 C

Anatase(TiO2)

900 C

Rutile(TiO2)

Orthorhombic Tetragonal Tetragonal

7/28/2019 3 Crystal

40/50

Examples of Monotropypolymorphism

Marcasite (FeS) Pyrite (FeS)Orthorhombic Cubic

Diamond (C) Graphite (C )Cubic hexagonal

3. Bond Types in Crystals Bonds are electrical forces that bind atoms in crystalline solids. Largely control physical properties (hardness, cleavage, melting T, and conductivity). Four major types. Most minerals in fact are combinations of the four types. Silicates are mostlyionic/covalent with some having weak van der Waals/hydrogen bonds as well. For example, MICAS: within sheets bonding is 50-50 ionic/covalent; bonds betweensheets are mostly weak ionic and/or van der Waals.

Ionic: One or more electrons are transferred to the outer shell of another element so they both have filled outer shells (inert configuration). Halite is Na+, Cl-; have electrical attraction that produces IONIC BOND. Physical properties of minerals with ionic bonds: soluble, moderate hardness and G,fairly high melting T, poor conductors of heat and electricity. Strength of ionic bonding is proportional to 1/r and q1q2, where r is interatomic distance between ions and q1, q2 is the valence of the two ions.

Covalent (strongest chemical bond): One or more electrons are shared in outer shells of two atoms to produce the inert electronic configuration. Physical properties of minerals with covalent bonds: insoluble, stable, moderate to veryhigh hardness, very high melting T, poor electrical conductors.

Metallic: Forces that arise from atoms that share electrons that from a cloudof e- around the atoms. No e- has affinity to any one atom and is free to movearound in structure. Physical properties of minerals with metallic bonds: soft,high plasticity, maleable, very conductive.

van de Waals: Polarization of atoms causes a weak dipolar attraction. Can bond together neutral molecules and essentially uncharged structural units bydeveloping small electrostatic forces on surfaces. Defines zones of cleavage,and low hardness in some minerals (clays, micas).

7/28/2019 3 Crystal

41/50

X-ray Diffraction Analysis and other TechniquesNature and production:

Prof. Gorring GEOS 443 MINERALOGY Oct. 22, 1998

X-Ray Diffraction

1. X-Ray Spectra X-Rays are only a small part of the electromagnetic spectum with wavelengths ( )ranging from 0.02 A to 100 A (A = Angstroms = 10 -8 m). X-Rays used to studycrystals have on the order of 1 to 2 A (i.e. Copper K = 1.5418 A). Visible lighthas much larger 's (4000-7200 A) and thus, x-rays are much more energetic (i.e. can

penetrate deeper into a material). This can easily be seen by inspection of theEinstein equation (E = h = hc/ ; E is Energy, frequency, c speed of light which isconstant for electromagnetic radiation, wavelength, h Plank's constant).

2. Diffraction and the Bragg Equation

Diffraction of an x-ray beam striking a crystal occurs because the of the x-ray beam is similar to the spacing of atoms in minerals (1-10 A). When anx-ray beam encounters the regular, 3-D arrangement of atoms in a crystal mostof the x-rays will destructively interfere with each other and cancel each other

out, but in some specific directions they constructively interfere andreinforce one another. It is these reinforced (diffracted) x-rays that producethe characteristic x-ray diffraction patterns that used for mineral ID.

W.L. Bragg (early 1900's) showed that diffracted x-rays act as if they were"reflected" from a family of planes within crystals. Bragg's planes are the rows of atoms that make up the crystal structure. These "reflections" were shown to onlyoccur under certain conditions which satisfy the equation:

n = 2dsin (Bragg Equation) where n is an interger (1, 2, 3, ......, n), the wavelength, d the distance betweenatomic planes, and the angle of incidence of the x-ray beam and the atomic planes.2dsin is the path length difference between two incident x-ray beams where one x-ray beam takes a longer (but parallel) path because it "reflects" off an adjacent atomic plane. This path length difference must equal an integer value of theof the incidentx-ray beams for constructive interference to occur such that a reinforced diffracted beam is produced.

For a given of incident x-rays and interplanar spacing (d) in a mineral, onlyspecific angles will satisfy the Bragg equation. Example: focus a monochromatic

x-ray beam (x-rays with a single on a cleavage fragment of calcite and slowlyrotate crystal. No "reflections" will occur until the incident beam makes an angle

7/28/2019 3 Crystal

42/50

that satisfies the Bragg equation with n = 1. Continued rotation leads to other "reflections" at higher values of and correspond to when n = 2, 3, ... etc.; theseknown as 1st, 2nd, 3rd order, etc., "reflections".

3. X-Ray Diffraction Techniques

Photographic plates were traditionally used to record the intensity and positionof diffracted x-rays. Modern systems use diffractometers which are electronicx-ray counters (detectors) that can measure intensities much more accurately.Computers are used to process data and make necessary complex calculations.

There are two main techniques. o Single-Crystal Methods : (x-ray beam is focused on a single crystal).

Primary application is to determine atomic structure(symmetry, unit cell dimensions, space group, etc.,).

Older methods (Laue method) used a stationary crystal with"white x-ray" beam (x-rays of variable ) such that Bragg'sequation would be satisfied by numerous atomic planes. Thediffracted x-rays exiting the crystal all have different and thus

produce "spots" on a photographic plate. The diffraction spotsshow the symmetry of the crystal.

Modern methods (rotation, Weissenberg, precession, 4-circle)utilize various combination of rotating-crystal and camera setupto overcome limitations of the stationary methods (mainly the #of diffractions observed). These methods use monochromaticx-rays, but vary by moving the crystal mounted on a rotatingstage. Usually employ diffractometers and computers for data

collection and processing. o Powder Methods: (x-ray beam focused on a powder pellet or powder smeared on a glass slide). Essential for minerals that do not form largecrystals (i.e. clays) and eliminates the problem of precise orientationnecessary in single-crystal methods.

Primary application is for mineral identification . Also can beused to determine mineral compositions (if d-spacing is afunction of mineral chemistry) and to determine relative

proportions of minerals in a mixture. Monochromatic x-rays are focused on pellet or slide mounted

on rotating stage. Since sample is powder, all possible

diffractions are recorded simultaneously from hypotheticalrandomly oriented grains. Mount is then rotated to ensure alldiffractions are obtained.

Older methods used photographic techniques. Most modernapplications employ X-Ray Powder Diffractometers.

4. X-Ray Powder Diffractometry

Uses monochromatic x-rays on powder mounted on glass slide that is attachedto a stage which systematically rotates into the path of the x-ray beam through

= 0 to 90. The diffracted x-rays are detected electronically and recorded on a inked strip

chart. The detector rotates simultaneously with the stage, but rotates through

7/28/2019 3 Crystal

43/50

angles = 2 . The strip chart also moves simultaneously with the stage anddetector at a constant speed.

The strip chart records the intensity of x-rays as the detector rotates through2 . Thus, the angle 2 at which diffractions occur and the relative intensitiescan be read directly from the position and heights of the peaks on the stripchart.

Then use the Bragg equation to solve for the interplanar spacings (d) for all themajor peaks and look up a match with JCPDS cards. JCPDS = JointCommittee on Powder Diffraction Standards.

CLASIFICATION OF MINERALS

We can classify the minerals into nine groups according to their chemical

compositions; these groups are:

1. Native elements.

The importants native elements are classified as follows:A- Trace metals consist of large number of crystals, each of which is

composed of closely packed atoms of the particular metallic element. Such a

crystal may be considered as an aggregate of positive ions immersed in gas "or"

cloud" of free electrons and attracted together by metallic bonding.

Many properties which are characteristic of metals, such as their opaqueness

and conductivity of heat and electricity' are due o the presence of the free

electrons. Examples: Gold, Silver, Copper, Iron, Nickel.B- Semimetals (carbon group) which includes tow natural forms of carbon,

diamond and graphite. Diamond is isometric with each carbon atom linked

tetrahedrally (covalent bonding) to four neighboring carbon atoms. In graphite

on the other hand, the carbon atoms lie in layers or sheets. Each sheet is covalent

bond together and every to sheets linked by Van Der Waal s (weak) bond.

7/28/2019 3 Crystal

44/50

2. SulphidesSulphides include a large group of minerals, with the general formula A m

Xp, in which X is Sulpher and A is the smaller metal atom. Examples: Galena

(PbS), Chalcopyrite (CuFeS2), Pyrite (FeS2) and .etc.

3. OxidesThis large class of minerals includes those compounds in which atoms or

cations, usually of one or more metals, are combined with oxygen that have ionic

bonding. Examples: Magnetite (Fe3O4), Chromite (Mg,Fe) Cr2O4, Hematite

(Fe2O3), Ilmenite (Fe TiO3), Rutile (TiO2) and Cassiterite (SnO 2).

4. HydroxidesThey have a layer structure in which each layer, parallel to (0001),

consists of two sheets of Oh with a sheet of Mg or Fe or Al atoms between them.

Examples: Brucite (Mg (OH)2), and Gibbsite (Al(OH)3).

5. Halides.The halides comprise those minerals which are primarily compounds of

the halogen elements (F, Cl, Br, I). Examples: Halite (NaCl) and Fluorite (CaF 2).

6. CarbonatesThe carbonates include some very common and widespread minerals in

which the fundamental anionic unit is (CO 3)2-

.Examples: Calcite (CaCO3), Dolomite (Ca, Mg (CO3)2), Aragonite (CaCO3),

Magnesite (MgCO3), Siderite (FeCO3), Witherite (BaCO 3).

7. SulphidesThey comprise a large number of minerals; some of which are anhydrous

e.g. Barite

7/28/2019 3 Crystal

45/50

8. PhosphatesThis group of minerals includes a large number of naturally occurring

oxysalts with an ionic group of (PO4)3- Examples: Monazite ((Ce, La, Y, Th) PO 4)

and Apatite (Ca 5 (PO4)3 F, Cl).

9. SilicatesThe silicates minerals are of greater importance than any other (nearly

$0% of the common minerals are silicates). The powerful bonds between the

oxygen and silicon ions are 50% ionic and 50% covalent.

In all silicate structures, the fundamental unit in the building of silicate minerals

is situated at the center of a tetrahedron whose corners are occupied by fouroxygen atoms.

Classification of the silicates is based on the different ways which the

SiO4 tetrahedra occur, either separately or linked together. On this basis we can

differentiate between 6 subgroups as given in the following table.

Structural Classification of Silicates

Subgroup StructurearrangementSi:ORatio Examples

Nesosilicates

single tetrahedrons(no Oxygens. shared betweenneighboringtetrahedra) joined by bonds with other cations

1:4

Olivine(Fe,Mg)2SiO4

Garnet (Ca,Fe,Mg)3(Al,Cr,Fe)2(SiO4)3

Sorosilicatestwo tetrahedrasharing oneOxygens.

2:7

EpidoteCa2Al2(FeO)(SiO4)(Si2O7)(OH)

HemimorphiteZn4Si2O7(OH)2.H2O

CyclosilicatesClosed rings of tetrahedra eachsharing 2 Oxygens.

1:3

Tourmaline(Na,Ca)(Li,Mg,Al)(Al,Fe,Mn)6(BO3)3

(Si6O18)(OH)4 Beryl

Be3Al2Si6O18

http://classes.colgate.edu/rapril/geol201/summaries/silicates/neso.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/soro.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/cyclo.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/cyclo.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/soro.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/neso.htm

7/28/2019 3 Crystal

46/50

InosilicatesSingle Chain

Continuous singlechainsof tetrahedrasharing 2 oxygens.

1:3

AmphibolesAnthophylite

Mg7(Si4O11)2(OH)2Hornblende

(Ca,Na)2-3(Mg,Al,Fe)5Si6(Si,Al)2O22(OH)2

InosilicatesDouble Chain

Continuous doublechainsof tetrahedrasharing alternatively2 then 3 oxygens.

4:11 PyroxeneEnstatiteMgSiO3

Phyllosilicates

Continuous sheetsof tetrahedroneach sharing 3oxygens.

2:5

Dioctahedral : Muscovite

KAl2(Si3Al1)O10(OH)2 Trioctahedral : Talc(Mg,Fe)3Si4O10(OH)2

Tectosilicates

Continuousframework of tetrahedra eachsharing all 4oxygens.

1:2 Quartz - SiO2

STRUCTURAL CLASSIFICATION OF SILICATES

1- NeosilcatesNeosilicates are those silicates with isolated (SiO4)4- groups in the

structure which are bound by cations only (ionic bonds). e.g. Olivine group,

Garnet Group, Aluminum Silicate group (Andalusite, Sillimanite, Kyanite and

Staurolite) and Zircon and Sphene.

Structure of Olivine (Mg, Fe)2 SiO4 is shown in ( Fig. 37) as example.

2- Sorosilicates In the sorosilicates two SiO4 tetrahedra are linked by sharing one

oxygen, forming (Si2O7)6- group in the structure (e.g Epidote and

Hemimorphite).

3- CyclosilicatesThe cyclosilicates are so named because they contain rings of linked SiO4

tetrahedra on either side, giving formula (SiO3)-2

n e.g. Tourmaline.

http://classes.colgate.edu/rapril/geol201/summaries/silicates/ino.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/ino.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/amphib.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/amphib.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/phyllo.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/tecto.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/tecto.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/phyllo.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/amphib.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/amphib.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/ino.htmhttp://classes.colgate.edu/rapril/geol201/summaries/silicates/ino.htm

7/28/2019 3 Crystal

47/50

4- InosilicatesThe inosilicates are a subclass in which the SiO4 tetrahedra are linked to

form chains of indefinite extent. There are two main types of chain structure.

A-

Pyroxene Group being single chain structures e.g. Enstatite andHypersthene (orthorhombic) and Diopside, Augite and Aegirine

(monoclinic) producing composition (SiO3)2-

Structure of diopside (Ca Mg Si2 O6) is shown in (Fig.40).

B- Amphibole Group being double chain structure. e.g. Anthophyllite

C- (Orthorombic) and Tremolite, Actinolite, Hornblend, Riebeckite

(monoclinic).

Structure of Tremolite (Ca 2 Mg5 Si8 O22 (OH)2) is shown in (Fig. 41). Cleavage of Pyroxene and Amphibole (Fig. 38 and 39). The bonding

between the chains is weaker than the bonding within the chains

themselves, and as a result both the pyroxenes and the amphiboles

have good prismatic cleavage (Fig. 38). The chains have trapezium-

shaped cross- sections (Fig. 39), the length of the which in the (b)

direction is double as in the amphibole as in the pyroxene. Cleavage

takes place in a diagonal manner, avoiding cutting through the chains

(broken line).

Properties Pyroxene Amphibole

b-dimension b-dimension is ~9 ; 1/2 thatof amphiboles

b-dimension is ~18 ; 2x that of pyroxenes

Chem. Comp. no OH- in structure (Not

contain OH- group)OH- in structure(contain OH- group)

FormGenerally blocky, prismaticcrystal habit(Short prismatic crystal)

elongate, splintery, acicular (rodshaped) habit(long prismatic crystal)

Cross Section 8- sided 6- sidedCleavage Angle 90 degree cleavage 60-120 cleavage

Extinction angle Large; 53 - 55 (exceptsoda types)Small; 15 - 25 (except sodatypes)

Colour weak Strong

7/28/2019 3 Crystal

48/50

Pleochrism weak Strong

Alteration Altered to amphiboles Altered to chlorite and other micas

Mode of occurrence

They are present in basic andultrabasic igneous rocks andare less abundant inmetamorphic rocks (highgrade)

They are more common inintermediate igneous rocks andmetamorphic rocks (mediumgrade)

Temperature form at high temperatures form at lower T than pyroxenes

Unit celldimintions

a b c9.73 8.91 5.25

a b c9.74 17.8 5.26

Si : O ratio No Present of OH-

Si : O = 1 : 3Present of OH- Si : O = 4 : 11

= Angstroms= 10-8cm.

5- PhyllosilicatesThe basic structural features of al minerals in this subclass is the presence

of SiO4 tetrahedra linked by sharing three of the 4-oxygens to form sheets with a

pseudohexagonal network. This sheets called tetrahedral layers of (Si 4O10)6- .

sometimes Al replace Si giving sheets of (AlSi4O10)5-

and (Al2Si4O10)6-

.In all phyllosilicates this tetrahedral layer id combined with another sheet

like grouping of cations( usually Al, Mg, or FeO in six-coordination with

Oxygen and Hydroxyl anions. six-coordination means that the anions are

arranged around the cations in an octahedral pattern, one anion at each solid

center of an octahedron and a cation at the center. By the sharing of anions

between adjacent octahedral a planer network results, and this is often known as

octahedral layer which has two surfaces or two sides (remember that octahedralrefers to the arrangement of the anions, not their number).

The mineral Gibbsite, Al (OH)3 and Brosite Mg (OH)2 (Fig.--), have this

type of structure, and the Al-OH layers and Mg-OH layers and Brosite layers,

respectively. The Gibbsite layer has dioctahedral arrangement, that is their

being three cations for each six OH anions.

The dimensions of the tetrahedral and the octahedral layers are closely

similar, and consequently, compose tetrahedral- octahedral layers are readily

formed either one tetrahedral and one octahedral layer (a two layer layers), or

7/28/2019 3 Crystal

49/50

an octahedral layer sandwiched between two tetrahedral layers (a three-

structure). Therefore, if only one surface of an octahedral layer is shared with a

tetrahedral layer, a two layer mineral results (e.g. kaolinite, Fig. 45); if both

surfaces are shared, a three layer is obtained (e.g. muscovite, Fig. 43).

Muscovite structure, KAl 2 (Al Si3) O10 (OH) 2As shown in Fig. 43, in the muscovite structure, on silicon of Si4O10 layers

is replaced by Al, and this increases the negative charge in the layers which is

balanced by the addition of positive ions (K) between the layers. The (Al Si3) O10sheets (tetrahedral layer) are arranged in pairs, with the apexes of their linked

tetrahedral pointing inwards in each pair (Fig.43).

The two sheets of a pair are linked together by Al cations which lie

between them. Each Al is octahedrally coordinated by 4-Oxygens belonging to

the two sheets and 2-OH. On the other hand, between on pair of sheets and the

next pair (between the bases of tetrahedra) lie the K ions, which are in 12-

coordination. This K-O bond is a much weaker bond (Van Der Waals bond)than the other bonds in the structure, and the perfect cleavage for which mica is

noted takes place along the layers of K ions, parallel to the sheet structure

muscovite is monoclinic.

The composite octahedral - tetrahedral layers are always staked in thedirection of the c axis in the crystal, in a, b plane the crystals are

pseudohexagonal symmetry. As shown in Fig. 44, the hexagonal symmetry of

each individual sheet is lost when two sheet are opposed to form a double sheet

(pair of sheets); linked by Al. the hexad axis of each single sheet passes through

the OH groups and since these to a pair of sheets, and the symmetry is lowered to

monoclinic.

6- Tectosilicates (Framwork)Tectosilicates includes some of the most important rock-forming

minerals, e.g. Quartz., Feldspars and Feldspathoide. Except quartz, all minerals

of the tectosilicates are aluminosilicatea in which Al replaces some of the Si in

tetrahedra to form excess negative charge. The cations which balance the

negative charge on the structure are always large ions (e.g. K, Na and Ca) with

coordination 8 or more and never smaller 6- coordination cation (e.g. Mg & Fe).

Slica group

7/28/2019 3 Crystal

50/50

Silica occurs in nature as three common minerals quartz, tridymite and

cristobalite Fig. 47.

Feldspars

The feldspars are the most abundant of all minerals. They are closely

related in form and physical properties, but they fall into two subgroups. The K-

Feldspars which are; monoclinic and the Na and Ca Feldspars (the plagioclases)

which are triclinic.

The general formula for the Feldspars Can be written W Z 4 O8, in which

W, may be; Na, K, Ca and Z, is Si and Al, the Si:Al ratio varying from 3:1 to 1:1.

4 point of great interest is the isomorphism between albite, NaAlSi3O8 and

anorthite CaAl 2Si2O8 of plagioclase series. The following species are recognized:K- Feldspar :

Sandine, KAlSi3O8

Orthoclase, KAlSi3O8

Microcline, KAlSi3O8 plagioclase series:

Albite, (Ab)NaAlSi3O8

Oligioclase, Ab6 An to Ab3 An

Andesine, Ab3 An to Ab AnLabradorite, Ab An to Ab An 3

Bytownite, Ab An3 to Ab An6

Anorthite, (An) CaAl2Si2O8

The structure of feldspars is a continuous three-dimensional

network of SiO2 and AlO4 tetrahedra with the positively charged Na, K

and Ca situated in the interstices of the negatively charged network.