Atomic structure, bondings and crystals

Matter

Each and every material is made of matter. A matter is composed of elements. further elements are clusters of atoms. An atom is the smallest part of a matter too small to see.

Elements

• Matter composed of single kind of atom is called element
• More than 100 elements found in nature, 92 produced by atomic reaction
• Classified as metal and non-metal

Compound

A compound is Composed of two or more elements combined chemically. Some compounds are calcium carbonate, water, glucose, etc

Atom

An atom is composed of sub-atomic particles(Nucleus, neutron, proton, electron). They can be seen through Ion Field Emission Microscopy, Scanning Electron Microscopy.

Atomic structure

The following fundamental particles are important from the subject point of view:

1.Electron: charge (-1.602×10^coulomb.).The mass of electron is 9.1^-31 kg

2. Proton: charge (1.602×10^coulomb.) The mass of a proton is 1.672×10^-27 kg
3. Neutron: no charge The mass of a neutron is 1.675×10-^27 kg

Molecule

• Molecule is defined as Smallest particle of substance that can exist freely
• Still exhibit all chemical properties of substance
• Consist of atoms(2 or more)

Mixture

Two or more elements or compounds physically combined in the same way in which two powders are mixed together Example: salt solution

Atomic Number

The atomic number of an element is numerically equal to the value of the positive charge on the nucleus of an atom or the number of protons present in the nucleus.Therefore, an atomic number of an element may also be defined as the number of electrons present outside the nucleus of its atom.

Atomic number = number of electrons = number of protons

Atomic weight

It is also called atomic mass or mass number. It is numerically equal to the sum of protons and neutrons in the nucleus.

The atomic weight is represented by A

Isotopes

Isotopes are actually the atoms of the same element but that have different atomic masses. To say simply, Isotopes of an element have the same atomic number but differ in their atomic mass number because, even though they have the same number of electrons and protons (electrically neutral), they differ in the number of neutrons.

Periodic Table

A periodic table is a tabular display of the chemical elements. The rows of the table in the table are called periods; the columns are respectively called groups.

Mendeleev’s Periodic Table

It was proposed by Mendeleev. As per this periodic table, "The physical and chemical properties of elements are a periodic function to its atomic weight."

Mendeleev arranged all the elements (known at that time) in the order of their increasing atomic weights in horizontal rows. The elements having similar properties come directly under one another in the same vertical columns or groups. In this table, the table was divided to seven horizontal rows (or periods) and eight vertical columns in total (or groups).

This table could not explain the position of isotopes. The isotopes were not given a separate place in the periodic table. The position of hydrogen was not fixed Lanthanides and actinides was not fixed.

Modern periodic Table

It was proposed by Mosely. As per this periodic table, "The physical and chemical properties of elements are a periodic function to its atomic number." Later on, the periodic table proposed by Mosley was modified by Bohr, which is now popularly known as Modern Periodic Table.

The position of isotopes was fixed. But it could not explain why lanthanides and actinides were kept away from the main body. The further position of hydrogen is also a contradiction in this table.

Binding Energy

Binding energy is defined as the mechanical energy required to disassemble a whole molecule or compound into separate parts. A bounded system has a lower potential energy than its constituent parts, this is what keeps the system together.

Atomic Bonds

Primary Bonds:

They are the strongest bonds which hold atoms together. There are three types of primary bonds

a) Metallic Bonds

This type of bond exists when each atom of the metal contributes its valence electrons to the production of an electron cloud that spreads all over the metal.

An important characteristic of the metallic bond is that the conduction of electricity and heat. These are produced by the free movement of valence electrons through the metal surface. These crystals are malleable and with variable hardness and melting point.b) Covalent Bonds

This bond is formed by sharing of equal electrons between adjacent atoms. An excellent example of covalent bonding is found in the chlorine molecule.

This bond is formed between those atoms or radical with similar electronegativity. Covalent crystals are characterized by poor electrical conductivity and high hardness.

c) Ionic Bonds

This bond exists between two unlike atoms. If an electron is transferred completely from a metallic atom to a non-metallic atom, thus formed two resulting ions are held together by the electrostatic force of attraction. Examples are the sodium and chlorine atoms.

These crystals have poor electrical conductivity, high hardness, and high melting point.

Secondary Bonds:

They are much weaker than primary bonds. They often provide a "weak link" for deformation or fracture. The examples for this type of bonds are:

a) Hydrogen Bond

Hydrogen bonding is the attraction between hydrogen in a highly polar molecule and the electronegative atom in another polar molecule. The highly electronegative element attract electron cloud density from the electropositive center.

It is responsible for causing ice to be less dense than water, an occurrence that allows ï¬Âshes to survive at the bottom of frozen lakes.

b) Van-der-Waals Bond

Inert gasses and molecules like methane, which have no valence electrons available for crystalline binding, obtain a weak attractive force as a result of polarization of electrical charges.

Elements possessing Van-der-Waals bond are soft, have poor electrical conductivity and low melting point.

Atomic arrangements

Crystal

The term ‘crystal’ of a material is defined as any small body having a regular polyhedral form , bounded by smooth surfaces, which are acquired under the action of its intermolecular forces. The crystals are also called as grains. The boundary that separates the two adjacent grains is called grain boundary.

Unit Cell

All crystal is composed of unit cells. A unit cell contains the smaller number of atoms, which taken together have the properties of the crystals of the particular metal. A unit cell is defined as the smallest parallelepiped which could be transposed in 3 coordinate directions to build the space lattice.

Lattice

The three-dimensional array formed by the unit cells of a crystal is called lattice.

Space lattice

It is defined as an array of points in three dimensions in which every point has surroundings identical to that every other point in the array. The distance between the atom- points is called inter-atomic or lattice spacing. Each point of a space lattice has identical surroundings.

Lattice parameters of a unit cell

lattice parameters can be described from a unit cell of a three-dimensional crystal lattice. It is formed by primitives or intercepts a, b and c along the three axes respectively. The three angles (α β and γ) are called interfacial angles

Types of Crystal Systems

There are in total 32 classes of crystal systems based on the geometrical consideration (i.e., symmetry and internal structure). But it is a common practice to divide these crystal systems into only seven groups or basic systems.

These seven basic crystal systems are:

Crystal structure

Body-Centered Cubic (B.C.C.):

In this type of crystal structure, the atoms are located at the corners of the cube and one atom at its center.

Total number of atom in a unit cell is =1 /8× 8 + 1 = 2

Atomic packing factor = 0.52

Face-Centered Cubic (F.C.C.):

In this type of crystal structure, the atoms are located at the corners of the cube and one atom at the center of each face.

Total number of atom in a unit cell is=1 /8× 8 +1/ 2× 6 = 1 + 3

= 4

Atomic packing factor = 0.74

Hexagonal Close Packed (H.C.P):

In this type of crystal structure, the cell has an atom at each of the twelve corners of the hexagonal prism, one atom is at the center of each of two hexagonal faces and three atoms in the body of the cell.

Total number of atom in a unit cell is= 3/2 + 3/2 + 3 = 6

Atomic packing factor = 0.74

Millers’ Indices

This is a system of notation of planes within a crystal of space lattice. These indices are based on the intercepts of different planes with the three crystal axes i.e. edges of the unit cell.

In particular, a family of lattice planes is found out by using three integers h, k, and â„“, called the Miller indices. Indices are written in the form of (h,k,â„“), and each index denotes a plane orthogonal to a direction given by (h, k, â„“) in the basis of the reciprocal lattice vectors.

The notation as represented {h,k,â„“} denotes the set of all planes that are also equivalent to (hkâ„“) by a symmetry of lattice.

In the context of crystal directions (not planes), the corresponding notations are: [h,k,â„“], denoted differently with square instead of round brackets, denotes actually the direction in the basis of the direct lattice vectors instead of the reciprocal lattice.

Allotropic and Polymorphic Transformation.

Polymorphism is defined as a physical phenomenon where any substance may have more than one crystal structure. Those substances that show polymorphism shows more than 1 type of space lattice in a solid state. The change in structure may be reversible if so the polymorphic change is known as allotropy. The crystal structure depends on both the temperature and the external pressure.

Imperfections in the atomic arrangement

Imperfections are the results of deformation which can be divided into two class.

1.Elastic Deformation

The term ‘elastic deformation’ may be defined as the process of deformation, which appears and disappears simultaneously with the application and removal of stress till elastic limits.

2. Plastic Deformation.

The term ‘plastic deformation’ may be defined as the process of permanent deformation, which exists in a metal, even after the removal of the stress. There are two basic modes of plastic deformation, namely slip or gliding and twinning.

The crystallographic defects are classified as follows:

1. Point Imperfections These defects are localized disruptions of the lattice involving one or possibly several atoms. The various types of point defects are discussed below:

i) Vacancy: Vacancy is produced when an atom is missing from a normal lattice point.

ii) Interstitial Defect: An Interstitial defect is formed when an extra atom within a crystal structure is inserted into the lattice structure at a site which is not a normal lattice point.

iii) Substitution Defect: A substitution defect is introduced when a foreign atom substitutes for a parent atom in the lattice

iv) Frenkel Defect: An ion dislodged from the lattice into an interstitial site is called Frenkel defect.

v) Schottky Defect: Whenever a pair of positive and negative ions is missing from a crystal, the defect caused is called Schottky defect. In such defect, the crystal is electrically neutral.

2. Line Imperfections

A linear disturbance of the atomic arrangement, which can move very easily on the slip plane through the crystal, is known as a dislocation. Two basic types of dislocations are:

i) Edge Dislocation: When a half plane atom is inserted between the planes of atoms in a perfect crystal, so formed defect so produced is known as edge dislocation. They are of 2 types i.e. positive and negative dislocation.

ii) Screw Dislocation: When atoms are displaced in two different planes perpendicular to each other, so formed defect is known as screw dislocation or imperfection.

3. Surface Imperfections

These defects are the two-dimensional regions in a crystal. These defects arise from a change in the stacking atomic planes on or across a boundary during arrangement.

i) External Defects: The exposed surface of any material is an imperfection itself, coz the atomic bonds do not extend beyond it. The atoms at the surface have neighbors on one side only, but atoms present inside the crystal have neighbors on both sides of them. Since atoms at the surface are not entirely surrounded by others, they actually possess higher energy than those of internal atoms.

ii) Internal Defects

a) Grain Boundaries :They are those imperfections which separate crystals or grains of different orientation in polycrystalline aggregation during nucleation or crystallization.

b) Twin Boundaries :It is a special type of grain boundary across which there is specific mirror lattice symmetry.

c) Tilt Boundary: Tilt boundary, in reality, is a series of aligned dislocations which tend to anchor dislocation movements normally contributing to plastic deformation.

d) Stacking Faults: It is a surface imperfection that arises due to the stacking difference of one atomic plane on another but the lattice on either side of the fault is perfect.

4. Volume Imperfections

Defects such as cracks may arise in crystals when there is only small electrostatic dissimilarity between the stacking sequences of a close packed plane in metals. The presence of a large vacancy or void space, when a cluster of the atom is missed then this case also called as a volume imperfection.

Deformation by Slip and Twinning

Comparison between Slip and Twinning

Slip Twinning

1. slip phenomenon occurs in discrete 1. Atom movements are much fewer

planes more than of atomic spacing . then the atomic spacing.

2. The orientation of the crystal above 2. Orientation difference takes place across

and below the slip plane is the same the twin plane. after deformation as before.

3. It occurs over wide planes. 3 . Every atomic plane is involved.

4.Slip begins when shearing stress 4. There is no critical resolved shear stress

on slip plane in the slip direction reaches a for twinning. threshold value called the critical resolvedshear stress.

5. It takes place in several milliseconds. 5. It takes place in a few microseconds.

Schmid’s Law

This law defines the relationship between shear stress and applied stress, and the orientation of slip phenomenon. This is an equation for finding the stress in slip plane given an axial force and angle of the slip plane.

Mathematically,

this is given by the relation :𝝉𝒓 = 𝝈 * 𝐜𝐨𝐬𝝍 * 𝐜𝐨𝐬𝝀

where 𝜆= Angle defining slip direction relative to the force,

𝜓= Angle defining the normal to the slip plane ,

ðœÂð‘Ÿ=Resolved shear stress in the slip direction

ðœÅ½ = Unidirectional stress applied to the cylinderFick’s First Law

Fick's first law actually relates the diffusive flux to the concentration under the assumption of steady state. This law postulates that the flux goes off high concentration to regions of low concentration, with a magnitude which is proportional to the concentration gradient.

𝑱 = −𝑫 *𝝏∅ /𝝏𝒙

J is called "diffusion flux",

D is known as diffusion coefficient,

∅ is called concentration at given instant

References:
1. D. R. Askeland, “The Science and Engineering of Materials”, PWS- Kent Publishing Co., Boston,
2. Westerman Table ( IS Standard)