Crystal Structure
Packing Spheres
Close-packed Structure
Crystal Defect
X-Ray Diffraction by Crystals
Miller Index
Types of Crystals
TKT2013 –noorshida mohd ali
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Crystal Structure and Bonding, Lecture notes of Inorganic Chemistry
An in-depth exploration of the various types of crystal structures, including simple cubic (scc), body-centered cubic (bcc), and face-centered cubic (fcc) systems. It delves into the packing of spheres, the counting of atoms within unit cells, and the relationship between lattice constants and atomic radii. The document also covers the different types of crystal forces, such as ionic, covalent, molecular, and metallic bonds, and their corresponding properties. Detailed explanations and examples are provided for specific crystal structures like rock-salt, cesium chloride, sphalerite, wurtzite, and fluorite. The document further discusses the concept of coordination number and the calculation of the number of ions in a unit cell. Overall, this comprehensive resource offers a thorough understanding of crystal structures, bonding, and their associated characteristics.
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2023/2024
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Crystal Structure
Packing Spheres
Close-packed Structure
Crystal Defect
X-Ray Diffraction by Crystals
Miller Index
Types of Crystals
1
2
CRYSTAL STRUCTURE
SOLID
CRYSTALLINE AMORPHOUS
- Having a regular and continuous three-dimensional arrangement of atoms in the solid state
- Possesses rigid and long-range order
- Its atom, molecules or ions occupy specific positions
- Accurate melting point
- Crystallization : process of forming crystals from a liquid or gas
- What forces responsible for the stability of a crystal? The periodic arrangement of atoms in the crystal - Having a random or disordered arrangement in the solid state, that is antithesis or opposite of crystalline - solid formed rapidly : glass - lack a regular three-dimensional arrangement of atoms - Inaccurate melting point 4
UNIT CELL
❖The smallest component of the crystal, which when stacked together with pure translation repetition reproduce the whole crystal ❖Basic repeating structural unit of a crystalline solid 5
triclinic
cubic
trigonal hexagonal tetragonal orthorhombic monoclinic
crystal
systems
7
8
CUBIC SYSTEM
LATTICE SYMBOL : PRIMITIVE UNIT CELL( P )
c a b
a, b, c = lattice constant (vectors)
, , = angles form by these vectors
x z y 10
CUBIC
SYSTEM
SIMPLE CUBIC
(SCC)
BODY-CENTRED
CUBIC (BCC)
FACE-CENTRED
CUBIC (FCC)
Unit cell :
primitive ( P )
Unit cell :
body-centred ( I )
Unit cell :
face-centred ( F )
11
COUNTING ATOM IN UNIT
CELL
Atoms in different positions in a cell are shared by differing numbers of unit cells CORNER/VERTEX: atom shared by 8 cells 1/8 atom per cell EDGE : atom shared by 4 cells 1/4 atom per cell FACE : atom shared by 2 cells 1/2 atom per cell BODY : unique to 1 cell 1 atom per cell An atom on a corner/vertex is shared by eight unit cells An atom on an edge is shared by four unit cells An atom on a face is shared by two unit cells , so only half of the atom belongs to each of these cells. 13
Cubic system Number of atom
Simple cube (SCC)
Body-centred cube (BCC)
Face-centred cube (FCC)
8 corners x 1/8 = 1 atom
(8 corners x 1/8) + 1 body = 2 atoms
(8 corners x 1/8) + (6 faces x 1/2) = 4 atoms
14
The relationship between the edge length ( a ) and radius (r)
of atoms in the simple cubic cell, body-centred cubic cell
and face-centred cubic cell
a = 2 r 16
b
2
= a
2
+ a
2
c
2
= a
2
+ b
2
= 3a
2
c = 3 a = 4r
a = 4r
b = 4r
b
2
= a
2
+ a
2
4r = a
2
+ a
2
4r = 2 a
a = 4r
17
CRYSTAL DENSITY
n = no of atom in one cell unit M = molecular weight of crystal N = Avogadro no. (6.023 x 1023 ) = density a = edge length = n x M a 3 N Gold (Au) crystallize in a cubic close-packed structure (the face-centred cube, FCC) and has a density of 19.3 g/cm^3. Calculate the atomic radius of gold = n x M a 3 N 19.3 g/cm 3 = 4 x 197. a^3 6.023 x 10^23 a^3 = 6.78 x 10 –^23 cm^3 a^3 = 6.79 x 10-^23 cm^3 x 1 x 10-^2 m 3 x 1 pm 3 1 cm 1 x 10
- 12 m a 3 = 6.79 x 10 7 pm 3 Step 1:get the volume 19
Step 1:get the mass of a unit cell and volume m = 4 atoms x 197.0 g Au x 1 mol 1 unit cell 1mol Au 6.023 x 1023 atoms m = 1.31 x 10-^21 g / unit cell V = m = 1.31 x 10
- 21 g / unit cell = 19.3 g/cm^3 6.79 x 10
- 23 cm 3 V = 6.79 x 10
- 23 cm 3 x 1 x 10
- 2 m 3 x 1 pm 3 1 cm 1 x 10-^12 m V = 6.79 x 10^7 pm^3 V = a^3 20