Introduc/on to solid

state chemistry

COURSE NAME: Solid State Chemistry

COURSE CODE: 4024582-2
 List of topics to be covered

1- Introduction to solid state chemistry

2- Study the crystal structures properties, crystal lattice, type of

crystals (covalent - ionic)- cubic centered face- cubic centered body.

3- Learn Bravais lattices

4- Study the symmetry operators , elements and axis of rotation,

symmetry and point group of molecules and point group of unit

cells-point groups and space groups

5- Calculate the volume of the unit cell , atomic radius , number of

molecules , close and square packing and the density. 1

 6- X- ray diffractions and Bragg's law
7- Crystal structure of solids: Solid crystallography- X-Ray
crystallography (interference phenomenon and diffraction method)
8- X-ray diffraction in the crystal structure - X-ray absorption- X-
Ray spectrum - experimental crystal study (Lewis method -
Rotatable crystal- powder diffraction)
9- How to calculate Miller indices of directions and planes-calculate
inter-planar d -spacing (dhkl)
The crystal binding in solid Material, lattice energy and ionic -10
.charge
.How to detect the crystal defects and types of defects -11
12- Effect of impurities on the properties of semiconductors

3
(n-type and p-type semiconductor). 2
Solid state Chemistry:
Solid state chemistry is concerned mainly with crystalline
inorganic materials, their synthesis, structures, properties and
applications.

A good place to begin is with crystal structures and crystal

chemistry. All necessary crystal structure information is contained
in data on unit cells, their dimensions and the positions or atomic
coordinates of atoms inside the unit cell.

3
 Types of Solids
There are two main types of solids
•Crystalline solid: well-ordered, definite arrangements of
molecules, atoms or ions.
• Crystals have an ordered, repeated structure.
• Polycrystalline material: comprised of many small crystals
or grains
•Amorphous solid: no definite arrangement of molecules, atoms,
or ions (i.e., lack well-defined structures or shapes).
• Amorphous solids vary in their melting points.

4
Types of Solids

5
 Some basic definitions
Lattice:
An infinite array of points in space, in which each point has
identical surroundings to all others.
Crystal Structure:
The periodic arrangement of atoms in the crystal.
It can be described by associating with each lattice point a group
of atoms called the MOTIF (BASIS).
Unit cell :
Is the smallest repeating unit in a crystal with all the symmetry
of the entire crystal.

6
 Some basic definitions
It can be also defined as the smallest component of the crystal,
which when stacked together with pure translational repetition
reproduces the whole crystal,
Three-dimensional stacking of unit cells is the crystal lattice.

The smallest repeating unit that

shows the symmetry of the
pattern is called the unit cell. 7
 The general features of a crystal

1. The presence of faces.

-well-formed crystals are found to be
completely bounded by flat surfaces.
-The surfaces are flat to a degree that gives Calcite
high-quality plane-mirror.

2- Crystals frequently cleave along preferred directions.

3- The crystals of a given material tend to be alike.

e.g. all needles, cubes, plates

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 The general features of a crystal

 The flatness of crystal surfaces can be attributed to the

presence of regular layers of atoms in the structure.

 and cleavage would correspond to the breaking of weaker

links between particular layers of atoms.

 Similarity of crystals indicates that the chemical nature of the

material plays an important role in determining the crystal
habit.

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 Seven crystal systems and Bravais lattices

3D lattices can be generated with three basis vectors.

They are infinite in three dimensions.
3 basis vectors generate a 3D lattice.
The unit cell of a general 3D lattice is described by 6 numbers
(in special cases all these numbers need not be independent)  6
lattice parameters (cell parameters)
 3 distances (a, b, c)
 3 angles (, , ).

1
 The Seven Crystal Systems
system Unit cell
Triclinic No special relation
abc All known
Monoclinic
α= γ = 90º ≠ β
crystals are
abc
Orthorhombic
α = β = γ = 90º found to be
a=bc
Tetragonal built up of one
α = β = γ = 90º

a=b=c of
Trigonal α = β = γ ≠ 90º
Or as hexagonal
7
a=bc
Hexagonal α = β = 90º,
γ = 120º Unit cells
a=b=c
Cubic
α = β = γ = 90º
1
 Bravais lattices

Bravais demonstrated that in a 3-dimensional system there are

fourteen possible lattices
Bravais lattice: is an infinite array of discrete points with
identical environment
seven crystal systems + four lattice centering types = 14 Bravais
lattices

1
 Four lattice centering types
No. Type Description
1 Primitive Lattice points on corners only. Symbol: P.
(each atom shared by 8 unit cells)
2 Base Centered Lattice points on corners as well as on centers of any
two parallel faces. Symbols: C
(corner atoms shared by 8 unit cells, face atoms
shared by 2 unit cells)
3 Face Centered Lattice points on corners as well as in the centers of
all faces. Symbol: F.
(corner atoms shared by 8 unit cells, face atoms
shared by 2 unit cells)
4 Body-Centered Lattice points on corners as well as in the center of
the unit cell body. Symbol: I.
(corner atoms shared by 8 unit cells, center atom
completely enclosed in one unit cell)

1
Arrangement of lattice points in the Unit Cell
& No. of Lattice points / Cell
Effective number of Lattice points per
Position of lattice points
cell

1 P 8 Corners = [8  (1/8)] = 1

8 Corners
2 I + = [1 (for corners)] + [1 (BC)] = 2
1 body center
8 Corners
= [1 (for corners)] + [6  (1/2)]
3 F +
=1+3=4
6 face centers
8 corners
+
4 C = [1 (for corners)] + [2  (1/2)] = 2
2 centres of opposite
faces

1
 P I F C
1 Cubic Cube   

I
P

a b c    90

Lattice point
F 1
 P I F C
2 Tetragonal Square Prism (general height)  

I
P

a b c
   90
1
 P I F C
3 Orthorhombic Rectangular Prism (general height)    

One convention
a b c
I
P

a b c
   90

F C
1
 P I F C
4 Hexagonal 120 Rhombic Prism 

a b c
  90 ,  120

A single unit cell (marked

in blue) along with a 3-unit
cells forming a hexagonal
prism
P I F C
5 Trigonal Parallelepiped (Equilateral, Equiangular) 

a b c
   90

1
 P I F C
6 Monoclinic Parallogramic Prism  

a b c
a b c   90 

P I F C
7 Triclinic Parallelepiped (general) 

a b c
  
2
 CLOSE-PACKING
Simple close packed structures (metals) Close packing in 2D, two
possible arrangements for a layer of such iden/cal atoms. On squeezing
the square layer in Figure (a), the spheres would move to the posi/ons
in Figure (b) so that the layer takes up less space.

(a)

(b)

22 21
Simple close packed structures (metals) Close
packing in 3D
3D close packing:
diTerent stacking sequences of close packed layers
Example 1: HCP Example 2: CCP

stacking sequence: AB stacking sequence: ABC

Polytypes: mixing of HCP and CCP, e. g. La, ABAC

22
1
 ‫الطبقتين‬
‫ومتمركزة‪A,B‬‬
‫بشرط‬ ‫ف‪..‬ى‬
‫الكيفي‪.‬ة‬ ‫الموجودة‬
‫متماثل‪..‬ة‬ ‫الفراغات‪..‬لبة‬
‫بنف‪.‬س‬ ‫‪.‬نق‪.‬كرات‬
‫الطبق‪.‬ةص‪A‬‬ ‫فو‬
‫فوق‬ ‫الثالث‪..‬ة‬
‫ع‪.‬‬ ‫الطبق‪..‬ة ‪B‬‬
‫عبارة‬ ‫الذرات‬
‫الطبق‪.‬ة‬ ‫توض‪..‬ع‬
‫ث‪.‬م‪.-‬ا ان‬
‫نرص‬ ‫اعتبرن‪.‬‬
‫‪-‬‬ ‫اذا‬
‫عل‪..‬ى‬ ‫ونحص‪..‬ل‬
‫تكون‬
‫تكون‬ ‫‪.‬ث‬
‫اى‬‫‪.‬‬
‫نبدا برص الطبق‪..‬ة‬‫‪,‬‬‫‪close packed structures‬‬
‫بحي‬‫تماما‪.‬‬
‫‪.‬ا‬
‫‪.‬ى‬‫‪.‬‬
‫ل‬ ‫الطبق‪..‬ة‬
‫لتنضيده‬
‫‪.‬ة ‪A‬‬
‫ا‪c‬و‬ ‫ق‬ ‫الطب‬‫‪.‬ن‬
‫‪.‬‬ ‫فوق‬
‫طريقتي‬
‫‪.‬ى‬ ‫ف‬ ‫الرابع‪..‬ة‬
‫‪.‬د‬
‫ذرات‬ ‫‪.‬‬ ‫الطبق‪..‬ة‬
‫يوج‬
‫ث`ث‬ ‫‪.‬ه‬ ‫‪.‬‬‫فان‬
‫‪.‬ا‬
‫ه‬ ‫تكون‬
‫‪.‬ة‬
‫في‬ ‫‪.‬‬ ‫وبذل‪..‬ك‬
‫الشبيك‬
‫ذرة‬ ‫نقاط ك‪.‬ل‬
‫ت`م‪.‬س‬ ‫حول‬
‫ان‬
‫الترتيب )‪ABCABC (FCC‬‬
‫مايمكن الفجوات فى الطبقة‪Ae‬‬ ‫اقلفوق احد‬ ‫التى بينها‬
‫الطبقة ‪B‬‬ ‫الفراغاتفى‬
‫كل ذرة‬
‫‪ A‬بحي‪.‬ث ك‪.‬ل ذرة‬
‫تحيط بها ‪ 6‬ذرات‬
‫‪A‬‬
‫‪B‬‬
‫‪c‬‬
‫‪AA‬‬ ‫‪A‬‬
‫‪B‬‬

‫‪c‬ضافة الطبقة الثالثة ‪ C‬يوجد احتمالين كما توضحه ا‪c‬شكال ‪:‬‬

‫‪24‬‬
‫‪ -‬توض‪..‬ع الطبق‪..‬ة الثالث‪..‬ة فوق الطبق‪..‬ة ا‪c‬ول‪..‬ى تمام‪..‬ا ونحص‪..‬ل عل‪..‬ى‬
‫الترتيب )‪ABAB (hcp‬‬
Close packed spheres of the same size in 3D is a li>le complicated.
This packing leads to possibility of two unique structures,
depending on how planes of 2D closest packed spheres are
layered. If every other layer is exactly the same then we has a so
called ABABA... structure. If not, then the structure is
ABCABCABC...The Jgures below shows the diKerence between
these two structures

24
The ABABAB structure (panel (b) in the Jgures above) is called the
Hexagonal Closest Packed (hcp) structure. In this structure, each
atom has 12 nearest neighbors and the volume of the spheres Jlls
the maximum possible space: 74.04%.

25
 CsCl Crystal construction

CsCl has a SC lattice of Cs+ ions with Cl- in

the center.
1 unit cell has 1 Cl- ion plus

(8 corners)(1/8 Cs+ per corner) = 1 net Cs+

ion.
Other Compounds:
CsBr, CsI, TlCl, TlBr,
TlI, NH4Cl

23
 NaCl construction

Na+ in
FCC lattice of Cl- with octahedral
Na+ in holes holes

2
Ion Count for the Unit Cell: 4 Na+ and 4 Cl- Na4Cl4 = NaCl
Can you see how this formula comes from the unit cell?

30
 The Sodium Chloride Lattice

Many common salts have FCC arrangements of anions (green

and large) with cations (red and small) in OCTAHEDRAL
HOLES — e.g., salts such as CA = NaCl
• FCC lattice of anions ----> 4 A-/unit cell

• C+ in octahedral holes ---> 1 C+ at center

+ [12 edges • 1/4 C+ per edge]
= 4 C+ per unit cell

16a–30 3
 Comparing NaCl and CsCl

• Even though their formulas have one cation and one

anion, the lattices of CsCl and NaCl are different.

• The different lattices arise from the fact that a Cs+

ion is much larger than a Na+ ion. 3

– NaCl Structure
• Each ion has a coordination number of 6.
• Face-centered cubic lattice.

• Cation to anion ratio is 1:1.

• Examples: LiF, KCl, AgCl and CaO.
– CsCl Structure
• Cs+ has a coordination number of 8.

• Different from the NaCl structure (Cs+ is larger than

Na+).
• Cation to anion ratio is 1:1.
33
 The CsCl and NaCl Structures

CsCl NaCl
16a–33 34
 Atomic packing factor
In crystallography, atomic packing factor (APF), packing efficiency or
packing fraction is the fraction of volume in a crystal structure that is
occupied by constituent particles. It is a dimensionless quantity and
always less than unity. In atomic systems, by convention, the APF is
determined by assuming that atoms are rigid spheres. The radius of
the spheres is taken to be the maximum value such that the atoms do
not overlap. For one-component crystals (those that contain only one
type of particle), the packing fraction is represented mathematically by

where Nparticle is the number of particles in the unit cell, Vparticle is the volume of
each particle, and Vunit cell is the volume occupied by the unit cell.

34 35