1. Introduction to Crystal 1. What is a crystal? 2. Lattice 3. Unit Cell 4. The 14 Bravais Lattices

Prof. Bondan T. Sofyan

Steel (metal)

Bridge high resolution transmission electron microscope (HRTEM)

1. What is a crystal?

Ferrite pearlite Prof. Bondan T. Sofyan

BCC (body centred cubic)

1. What is a crystal?

HRTEM

Periodic arrangement of atoms CRYSTAL

{111}α plates

small particle

(111)α

(111

)α

(002)α

0.23 nm

vertical fin (aluminium)

optical microscope

50 nm

θ'

Ω

(111

)

(111)

(002)

Ω

Ω

small particle

transmission electron microscope (TEM)

1. What is a crystal?

Prof. Bondan T. Sofyan

{111}α plates

small particle

(111)α

(111

)α

(002)α

0.23 nm

(HRTEM) (111

)

(111)

(002)

Aluminium

0.23 nm

1. What is a crystal?

Prof. Bondan T. Sofyan

Periodic arrangement of atoms

FCC (face centred cubic)

1. What is a crystal?

CRYSTAL

Prof. Bondan T. Sofyan

So, what is a crystal ?

•  A crystal is a solid consisting of a three-dimensional periodic ordering of atoms, ions or molecules.

•  Kristal adalah padatan yang atom-atomnya, ion-ionnya atau molekul-molekulnya berada dalam susunan 3 dimensi yang teratur.

•  This kind of solid is then termed as: crystalline solid (padatan kristalin), while at the other end, the solid, which does not have a periodical ordering of atoms, is called amorphous solid (padatan amorf).

•  Most metals (Al, steel, Cu and their alloy (paduan)) are crystalline. While glass and most polymers (plastics, rubber, etc) are amorphous.

Prof. Bondan T. Sofyan

There are two kinds of crystalline solid: –  Single crystal (kristal tunggal), where ALL atoms in

that material arrange themselves in one direction only.

–  Polycrystal (polikristal). This material consists of several group of atoms (grains) that have different orientation to each other.

1. What is a crystal?

Prof. Bondan T. Sofyan

Single crystal

Polycrystal

GRAIN (BUTIR)

In one grain, atoms are oriented at the same direction

Prof. Bondan T. Sofyan

2. Lattice (Kisi) •  As explained before, a three-dimensional periodic

arrangement of atoms, ions or molecules is always present in all crystals. If each atom is represented by a point (its centre of gravity), the arrangement is called a lattice.

Three-dimensional periodic arrangement of atoms in a crystal

The lattice of the crystal Prof. Bondan T. Sofyan

•  A Lattice is a three dimensional arrangement of points in which all of the points have identical surroundings

•  Kisi adalah susunan titik-titik dalam ruang tiga dimensi

sedemikian rupa sehingga setiap titik memiliki lingkungan yang sama.

2. Lattice (Kisi)

Prof. Bondan T. Sofyan

•  A Unit Cell is the fundamental or most primitive unit of the lattice.

•  Sel satuan adalah satuan (unit) terkecil dari kisi.

•  From the above illustration, the fundamental unit of the lattice is a (simple) cubic. Therefore, it is said that the unit cell of the lattice is simple cubic.

3. Unit Cell (Sel Satuan)

Prof. Bondan T. Sofyan

•  The unit cell is defined as having crystallographic axes (sumbu kristalografi), which may be described in terms of their length (panjang) a, b & c and the angles (sudut) α, β and γ. These lengths and angles are referred to as the Lattice Parameters or Lattice Constants of the unit cell.

•  For lattice parameters, although we could use special

values of a, b and c and α, β and γ to generate a variety of lengths, shapes etc. only SEVEN types of cell are necessary to describe all crystals and called: The Seven Crystal System. Hanya ada TUJUH jenis sel satuan untuk seluruh jenis kristal yang ada di alam. Ini disebut: Tujuh Sistem Kristal.

3. Unit Cell (Sel Satuan)

Prof. Bondan T. Sofyan

•  The 7 crystal systems correspond to 7 point lattices (simply by putting points at the corners of the unit cell). However, there are other arrangements of points that satisfy the requirements of a point lattice. Bravais demonstrated that there are in fact 14 possible point lattices and no more.

•  One (Seseorang) may therefore consider that the 14

Bravais lattices (or point lattices) fall into 7 fundamental classes.

•  We distinguish the 14 Bravais lattices on the basis of

Simple (or Primitive), and Non-Primitive.

3. Unit Cell (Sel Satuan)

Prof. Bondan T. Sofyan

•  Simple or primitive lattices have one lattice point (or atom) per unit cell.

•  Non-Primitive cells have > 1. •  A lattice point at the interior (di dalam) of a cell belongs

to the cell. Lattice points in a cell face are shared (dibagi) by two cells. Lattice points on the corner are shared by 8 cells.

•  The number of lattice points per unit cell will be given by:

N = Ni + Nf/2 + Nc/8

3. Unit Cell (Sel Satuan)

Prof. Bondan T. Sofyan

Prof. Bondan T. Sofyan

Cubic Three equal axes at rightangles.a=b=c. α=β=γ=90°

SimpleBody-centredFace-centred

PIF

Tetragonal Three equal axes at rightangles, two equal.a=b≠c. α=β=γ=90°

SimpleBody-centred

PI

Orthorhombic Three unequal axes at rightangles.a≠b≠c. α=β=γ=90°

SimpleBody-centredBase-centredFace-centred

PICF

Rhombohedral(trigonal)

3 equal axes, equally inclined.a=b=c. α=β=γ≠90°

Simple R

Hexagonal Two equal, coplanar axes at120°, 3rd axis at right angles.a=b≠c. α=β=90°, γ=120°

Simple P

Monoclinic Three unequal axes, one pairnot at right angles. a≠b≠c. α=γ=90°≠β

SimpleBase-centred

PC

Triclinic Three unequal axes, unequallyinclined, none at right angles.a≠b≠c. α≠β≠γ≠90°

Simple P

3. Unit Cell (Sel Satuan)

Prof. Bondan T. Sofyan

a

Simple (P)

Body-centred (I)

Face-centred (F)

4. The 14 Bravais Lattices

Cubic

Prof. Bondan T. Sofyan

Tetragonal

Simple (P) Body-centred (I)

a a

c

4. The 14 Bravais Lattices

Prof. Bondan T. Sofyan

Orthorhombic

c

a b Simple (P) Body-centred (I)

Base-centred (C) Face-centred (F)

4. The 14 Bravais Lattices

α a

Rhombohedral (R) Hexagonal (P)

120º

c

a

4. The 14 Bravais Lattices

Prof. Bondan T. Sofyan

Monoclinic

β a b

c

Simple (P)

Base-centred (C)

4. The 14 Bravais Lattices

Prof. Bondan T. Sofyan

Triclinic

α β

γ a

b

c

4. The 14 Bravais Lattices

Simple (P) Prof. Bondan T. Sofyan