## Saturday, June 6, 2015

### 2. Solid State - JEE Main - Core Revision Points

Importance of  Core Revision Points: Core Revision Points are important because if you remember them strongly, many more points related to them will come out of your memory and help you to answer question and problems. Read them many times and make sure you remember them very strongly.

## JEE Syllabus (2015)  on Solid State Topic

Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids,   Bragg’s Law and its applications; calculations involving unit cell parameters, imperfection in solids; Electrical, magnetic and dielectric properties.

Jauhar, CBSE XII class

## Sections in the Chapter

2.1 Space Lattices and Unit Cell
2.2 Close Packing in Crystalline Solids
2.3 Interstitial Sites or Interstitial Voids
2.4 Types of Cubic Crystals and Number of Atoms per Unit Cell
2.5 Experimental Methods of Determining Crystal Structure: X Rays Diffraction
2.6 Coordination Number and Radius Ratio
2.8 Calculation of Density of a Crystal from its Structure
2.9 Structures of Ionic Compounds
2.10 Imperfections in solids
2.11 Properties of solids
2.12 Amorphous solids

## Solid State - Revision Points

The main content covered in the chapter is about the formation of crystals in solids. Last section 2.12 is about amorphous solids which are not crystalline solids.

Solids can be broadly classified into two categories: crystalline and amorphous.

### Crystalline solids

The outstanding features are its flat faces and share edges which in a well developed form are usually arranged symmetrically.  Therefore, there is a high degree of internal order throughout the crystal. There is a definite pattern constantly repeating in space that forms the crystal. This order in the crystal is known as long-range order.

### Amorphous solids

Amorphous solids are not crystals and they do not have long range order but have short-range order. An ordered arrangement exists around some atoms, molecules or ions only up to short distances. The same order will not be found around other atoms or molecules in the solid at another place. In many was amorphous solids are more closely related to liquids and are therefore regarded as supercooled liquids with high viscosity.  Some crystalline materials can be converted into amorphous or glassy form by rapidly cooling the melt. Freezing the vapours also gives rise to amorphous solids.

## Bonds Present in  Solids

Molecular bonds:  In these solids, the constituent particles are molecules. The molecules are held together by weak Van der Waals forces. Examples are iodine, ice and solid carbon dioxide.

Ionic bonds:  Ionic solids have positively and negatively charged ions which are arranged in crystal form and held together by strong electrostatic forces. Examples are salts like NaCl, NaNO3, LiF and Na2SO4 etc.

Covalent bonds:  In these solids, the constituent particles are atoms and they are held together by covalent bonds. Examples are diamond, silicon carbide, and silica.

Metallic bonds: In solids with metallic bonds, positive kernels are immersed in a sea of mobile electrons. The forces between the constituents, positive kernels and electrons form the metallic bonds. These bonds are present in metals like copper, nickel etc.

## 2.1 Space Lattice and Unit Cell

The crystalline solids have their constituent particles - molecules, ions or atoms at specific locations in a three dimensional space, the basic shape of which repeats many times to form the crystalline solid.  The arrangement of this infinite set of points at which the constituent particles of the solid exist is called space lattice.

### Space Lattice

A space lattice is a regular arrangement of the  constituent particles of a crystalline solid in three dimensional space. These points are called lattice points.

### Unit Cell

A unit cell is the smallest repeating unit in space lattice.

### Parameters to describe a unit cell

Six parameters are required.  The unit cell is assumed to be formed of straightline in three axes.

These the three basic vectors along three crystallographic axes are termed (a,b, and c). Three angles are there between the crystallographic axes (α,β,γ). The angle α is between the edges b and c, The angle β is between edges c and a. The angle γ is between the edges b and a.

### Seven Crystal Systems

Crystals can be classified into seven categories

Triclinic -  a is not equal to b  is not equal to - (α,β,γ) are different and not equal to 90 degrees

Monoclinic

Orthoclinic

Trigonal or Rhombohedral

Cubic

Tetragonal

Hexagonal

2.2   Close Packing in Crystalline Solids

In the formation of crystals, closed packing of the constituent particles takes place.

Square Pattern

To understand arrangement of the particles in a solid one can visualise four particles arranged as a square. In this one particle assumed as a sphere is above another particles and four such sphere form a square and the pattern is repeated. But this pattern is not the usual pattern because only 52.4% of the available space becomes occupied in this square pattern of packing.

Hexagonal Pattern

In hexagonal close packing of particles (assumed as spheres), the spheres in the second row are placed in the depressions between the spheres in the first row. (In earlier square pattern, a sphere is placed on another sphere. But now a sphere is placed in the depression between two spheres in  the row below. In this packing, 60.4% of space gets occupied. Hence this hexagonal close packing gives more close packing.

Co-ordination Number

The number of spheres which are touching a given sphere in packing arrangement is called co-ordination number. Thus in two dimensional representation coordination number is 4 in square arrangement and six in hexagonal arrangement.

2.3 Interstitial Sites or Interstitial Voids

In the packed structure of the crystalline solid, there are hollow spaces between particles. These holes are voids are called interstitial sites or interstitial voids. Two important interstitial sites are 1. Tetrahedral interstitial site.  (2) Octahedral interstitial site.

2.4 Types of Cubic Crystals and Number of Atoms per Unit Cell

There are three common types of cubic crystals.

1. Simple cubic
2. Body centred cubic
3. Face centred cubic or cubic close packing

## 2.5 Experimental Methods of Determining Crystal Structure: X Rays Diffraction

The structure of solid is studied by X-ray diffraction methods.

Bragg Equation:

n lamba = 2d sin theta

where d = distance between the planes of the constituent particles of the  crystal.
lamba = wave length of the x-ray used.
n =  1,2,3 etc.  standing for the serial order of the diffracted beam.

2.6 Coordination Number and Radius Ratio
2.8 Calculation of Density of a Crystal from its Structure
2.9 Structures of Ionic Compounds
2.10 Imperfections in solids
2.11 Properties of solids
2.12 Amorphous solids

close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices;

packing of crystals;
Body centred cubic(bcc),
Hexagonal closed packed (hcp) and

cubical close packed (ccp)

Point defects: Schottsky defects, Frenkel defects

See an Oxford Video on Crystal Structure
09. Geometry of Solids I: Crystal Structure in Real Space
http://podcasts.ox.ac.uk/09-geometry-solids-i-crystal-structure-real-space

Good Websites for Solid State Topic

Updated 6 June 2015
Originally published  22 May 2015

### Good Websites for topic Solid State - Chapter Two in Jauhar

Oxford Video on Crystal Structure
09. Geometry of Solids I: Crystal Structure in Real Space
http://podcasts.ox.ac.uk/09-geometry-solids-i-crystal-structure-real-space

https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Structure/solidstate.htm

http://www.seas.upenn.edu/~chem101/sschem/solidstatechem.html

Future use of the material in this topic

The material is solid state is further useful in the topic of Solid State Electronics - Semiconductors

The website below was not found when checked on 6 June 2015

http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Strucsol.html

Contents

Lecture 1. Fundamental Aspects of Solids & Sphere Packing.

1. Why Study Solids?

2. Some crystallographic ideas

lattice (lattice types)
motif (basis)
crystal structure
unit cell (counting atoms in unit cells)
fractional coordinates
coordination number

3. Representations of structures

Perspective (Clinographic)
Projection (Plan) diagrams

4. Close-Packing of spheres

hexagonal close packing (hcp)
cubic close packing (ccp)

5. Structures of metallic elements

6. Interstitial sites in close-packed arrangements

Updated 6 June 2015
Originally posted  1 June 2007