Electron Diffraction

Electyron Diffraction refers to the wave nature of electrons. However, a from of technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern. This phenomenon is commonly known as the wave particle duality, in which it states that the behavior of a particle of matter (in this case the incident electron) can be described by a wave. For this reason an electron can be regarded as a wave, like sound or water waves. This technique is similar to X-ray and neutron diffraction.

Electron diffraction is most frequently used in the solid state physics and chemistry to study the crystal structure of solids. Experiments are usually performed in the transmission electron microscope (TEM), or a scanning electron microscope (SEM) as electron back scatter diffraction. In these instruments electrons are accelerated by electrostatic potential in order to gain the desired energy and determine their wavelength before they interact with the sample to be studied.

Electron Diffraction in Materials Science

Electron diffraction is an very important technique for crystallographic characterization, a valuable complementary tool to powder and single crystal X-ray diffraction.

Applications include phase identification and precision determination of suitable structural details for crystals in the micrometer to nanometer size range.

Electron Diffraction with the PDF-4+ Database

• The PDF-4+ database can be used to generate two types of electron diffraction patterns for all PDF entries with atomic coordinates:
  1.   Transmission electron spot patterns
  2.   Electron back scattering patterns
• To illustrate electron diffraction pattern generation with the PDF-4+ database, Iron (Fe, face centered
• cubic (FCC), space group Fm-3m) will be used as an example.
• The PDF-4+ database cannot perform search-match procedures directly on digital electron diffraction patterns, they must first be indexed to obtain a d-spacing-intensity (d/I) list. Search-match procedures can then be performed using SIeve+.
• Electron diffraction patterns generated by the PDF-4+ database do not account for intensity variation due to either sample or instrumental effects.

Term Diffraction

Introduction
The term diffraction in the case of waves refers to their bending round the obstacles. When the obstacle is large compared to the wavelength no wave bends around the edges of the obstacle. When the size of the obstacle is small compared to the wavelength of the light waves bend round the edges of the obstacle. When the size of the obstacle is very very small the waves bend round it so that we find no practical effect on the wave. The diffraction phenomena is more predominant when the size of the obstacle is small and is comparable with the wavelength of the incident light.
                                  
 One of the examples of diffraction phenomena is that when a beam of light passes from a narrow slit it spreads out to certain extent in the geometrical shadow.
                                               
In the above figure an obstacle AB with a straight edge is place in the path of a light wave spreading from a narrow slit illuminated by a monochromatic light source. The straight edge A is parallel to the slit S. The geometric shadow of edge A on the screen C is not sharp. A small portion of the light bends around the edge A into the geometrical shadow below the point C. Intensity gradually decreases as we enter into the shadow below C. As we go above C, the intensity alternately increases and decreases; several bright and dark bands parallel to the edge are observed. These bands are called diffraction pattern. The width of these bands goes on decreasing as we go upwards and uniform illumination is observed farther away from C

Term Diffraction : Pattern

                        
    A very small circular disk of diameter AB obstructs the path of (rays) waves emerging from a point source S. The diffraction pattern is observed on the screen SC. If the light propagates in straight line there would be a shadow of diameter CD on the screen. If the distance between the disk AB and the screen CD is great enough, we find diffraction pattern consisting of alternating dark and bright rings with a bright circular spot at the centre at 'O'.

Term : Diffraction

The diffraction phenomena is observed when the condition l `~~` b² / 4`lambda`  is satisfied, where l is the distance between the object and the screen, b size of th object an d`lambda`  is the wavelength of light obstructed by the object. There is a little difference between the formation of interference and diffraction patterns, though superposition of waves is involved in both the cases. Interference is the result of superposition of light waves emitted by two or more number of separate coherent sources, where as diffraction is due to superposition of light wavelets originating from every point of a wavefront which act as infinitely small coherent sources. Diffraction effects are observed only when a portion of the wave front is obstructed by the obstacle.

Electron diffraction pattern

Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern. This phenomenon is commonly known as the wave-particle duality, which states that the behavior of a particle of matter (in this case the incident electron) can be described by a wave. For this reason, an electron can be regarded as a wave much like sound or water waves. This technique is similar to X-ray and neutron diffraction.

Electron diffraction is most frequently used in solid state physics and chemistry to study the crystal structure of solids. Experiments are usually performed in a transmission electron microscope (TEM), or a scanning electron microscope (SEM) as electron backscatter diffraction. In these instruments, electrons are accelerated by an electrostatic potential in order to gain the desired energy and determine their wavelength before they interact with the sample to be studied.

Most electron diffraction is performed with high energy electrons whose wavelengths are orders of magnitude smaller than the interplanar spacings in most crystals. For example, for 100 keV electrons l < 3.7 x 10-12 m. Typical lattice parameters for crystals are around 0.3 nm.

Electrons are charged, light particles and their penetration into solids is very limited.LEED and RHEED are therefore considered to be surface science techniques, while transmission electron diffraction is limited to specimens less than 1 mm thick. Transmission electron diffraction is usually carried out in a transmission electron microscope (TEM).

Features of electron diffraction

There are three particularly important features of diffraction using high energy electrons:
(1) Since l is very small, Bragg angles are also small, so the Bragg Law can be simplified to:
    l = 2dqB
(2) The diameter of the Ewald sphere is very large compared to the size of the unit cell in the reciprocal lattice.
(3) Lenses are able to focus the diffraction pattern and to change the camera length, which is equivalent to moving the film in an x-ray experiment.

Total ionic equation

Ions are formed when electrons are either added or removed from the atoms. Chemical reactions are represented by simple molecular formulas. However the reactions actually take place by means of ions.
When reactions take place in aqueous medium that is, in presence of water, the atoms in the molecule either gain or lose electrons to form ions. These ions then combine with other ions to form resultant products. Generally the reactions are not shown as taking place by means of ions. However when done so, it is called total ionic equation.

Introduction to Total ionic equation:

Following denotions are used while writing the ionic equation.
(l) in the subscript  means the compound is in its liquid state,
(s) in the subscript means solid state.
(g) in the subscript means gas state.
The ionic reactions are single or double displacement reactions and are possible only with electrolytes.

Total ionic equation: Illustration-I

Let us consider a reaction of iodine precipitation from bromine and sodium iodide.
Br2_(l) + 2 NaI_(aq) -----------> 2 NaBr_(aq) + I2_(s)
Bromine exists as liquid at room temperature hence marked (l).
Sodium iodide being an ionic compound, would dissociate into ions in water, hence represented by (aq), same about sodium bromide too.
However the iodine molecule in the products is insoluble in water and hence shown as solid which precipitates.
To write the total ionic equation, write the ionic forms as
2NaI ------------>2 Na⁺_(aq) +2 I^-_(aq)
Br2--------------->2Br^-_(aq)
Also in the products,
2 NaBr_(aq)---------------> 2 Na⁺(aq) + 2 Br^-_(aq)
Thus the total ionic equation is written as
Br_2(l) + 2 Na⁺_(aq) +2 I^-_(aq) ----->  2 Na⁺(aq) + 2 Br^-_(aq) + I2(s).

Total ionic equation: Illustration-II

Consider another example of formation of silver chloride from silver nitrate
CaCl_2(aq) + 2AgNO_3(aq) Ca(NO₃)_2(aq) + 2AgCl_(s)

The dissociation would be
CaCl_2(aq)--------------> Ca²⁺_(aq) +2Cl⁻_(aq)
2AgNO_3(aq)-----------------> 2Ag⁺ _(aq)+ 2NO₃⁻_(aq)
    Thus the total ionic equation would be:

Ca²⁺_(aq) + 2Cl⁻ _(aq)+ 2Ag⁺_(aq) + 2NO₃⁻_(aq) Ca²⁺_(aq) + 2NO₃⁻ _(aq)+ 2AgCl_(s)

Writing net ionic equations

Ions are formed when electrons are either added or removed from the atoms. Chemical reactions are represented by  simple molecular formulas.  However the reactions  actually take place by means of ions.

When reactions take place in aqueous medium that is, in presence of water, the atoms in the molecule either gain or loose electrons to form ions.  these  ions then combine with other ions to form resultant products. Generally the reactions are not shown as taking by means of ions.However when done so,it is called total ionic equation.

Following denotions are used while writing the ionic equation.
(l) in the subscript  means the compound is in its liquid state,
(s) in the subscript means solid state.
(g) in the subscript means gas state.

Illustration of writing net ionic equations

2NaI _(aq) +Br2 _(aq)--------------->2NaBr _(aq) +I_2(s)
 (aq) Bromine exists as liquid at room temperature hence marked (l).
Sodium iodide being an ionically bonded compound,would dissociate into ions in water ,hence represented by (aq), Same about sodium bromide too. However the iodine molecule in the products is insoluble in water and hence shown as solid which precipitates.
To write the total ionic reaction,write the ionic forms,
2NaI ------------>2 Na⁺_(aq) +2 I^-_(aq)
Br2--------------->2Br^-_(aq)
Also in the products,
2 NaBr_(aq)---------------> 2 Na⁺(aq) + 2 Br^-_(aq)
Thus the total ionic reaction is written as
Br_2(l) + 2 Na⁺_(aq) +2 I^-_(aq) ----->  2 Na⁺(aq) + 2 Br^-_(aq) + I2(s),
But since some ions i.e.Na⁺(aq) are present on both sides,they can be said to have not taken part in the reaction and hence treated as spectator ions. So if we overlook these ions from both sides,

The net ionic reaction is :-
Br_2(l) + 2I-_(aq) -----> 2Br-_(aq) + I_2(s)
Br_2(l) + 2 Na⁺_(aq) +2 I^-_(aq) ----->  2 Na⁺(aq) + 2 Br^-_(aq) + I2(s)

Illustration II of writing net ionic equations

Consider another example of formation of silver chloride from silver nitrate
CaCl_2(aq) + 2AgNO_3(aq) Ca(NO₃)_2(aq) + 2AgCl_(s)
The dissociation would be
CaCl_2(aq)--------------> Ca²⁺_(aq) +2Cl⁻_(aq)#
2AgNO_3(aq)-----------------> 2Ag⁺ _(aq)+ 2NO₃⁻_(aq)
    Thus the total ionic equation would be:
Ca²⁺_(aq) + 2Cl⁻ _(aq)+ 2Ag⁺_(aq) + 2NO₃⁻_(aq) Ca²⁺_(aq) + 2NO₃⁻ _(aq)+ 2AgCl_(s)
The net ionic reaction is
Ca²⁺_(aq) + 2Cl⁻ _(aq)+ 2Ag⁺_(aq) + 2NO₃⁻_(aq) ---------> Ca²⁺_(aq) + 2NO₃⁻ _(aq)+ 2AgCl_(s)
2Cl⁻ _(aq)+ 2Ag⁺_{(aq)------------------>} 2AgCl_(s)

Naming ionic and molecular compounds

A chemical compound has a unique and defined chemical structure in which fixed ratios of atoms are held together in a defined spatial arrangement by chemical bonds. Basically there are two types of chemical compounds in chemistry, namely

Ionic compounds: Any substance which consists of two or more ionically-bonded atoms is called ionic compounds. A good example of an ionic compound is sodium chloride (table salt). In ionic compound, ions are held together in a lattice structure by ionic bonds. Positively charged ions are called cations and negatively charged ions are called as anions.


Molecular compounds: A molecule is the basic unit of a molecular compound. A molecule is defined as an object containing two or more atoms bonded together by covalent bonds. A molecule is the smallest particle of a compound which defines the properties of that compound. When a molecule is dissolved, it never dissociates.

naming ionic compounds

Ionic compounds dissolve in polar solvents which ionize, such as water and ionic liquids. They are also capable of dissolving in other polar solvents like alcohols, acetone and dimethyl sulfoxide. Ionic compounds do not tend to dissolve in non polar solvents.
According to International Union of Pure and Applied Chemistry IUPAC names of any ionic compound is written in two words. First name contains cation with oxidation number written in parentheses followed by the name of the anions. For example, the name of Fe₂ (so₄)₃  is written as iron(III) sulfate.

naming molecular compounds

We use chemical formula to describe the constituents of any chemical compound. Basically, there are three types of chemical formula namely, simple formula, graphic formula, and structural formula.

Simple formula:
In this formula, the elements are represented in symbolic form with subscripts to describe their ratio. Consider the simple formula of water which is H₂o. It shows the presence of two parts hydrogen and one part of oxygen.

Graphic formula:
In graphical formula, the element is represented in such a way to show the physical orientation of the constituent atoms to one another. The graphic formula of water is HOH. Water molecule has an atom of hydrogen to either side of an atom of oxygen.

Structural formula:
In structural formula, each and every atom is two dimensionally represented. The structural formula for water is given by H-O-H.

An example of a compound

An example of a compound is the common salt in pure form.
The molecular formula or the chemical formula of this compound is NaCl and it's a pure homogeneous compound.

The general physical appearance of this compound is :
it is white , crystalline in nature.The taste of this compound as we are all  familiar with:  it is salty.
The given compound is a salt and  is called sodium chloride.
This  chemical species is  called a compound, because of the following reasons:
It cant be separated into its constituent elements by any physical means and
the properties of this compound are totally different from the properties of its constituent elements.

why NaCl is a compound

     1) NaCl is a compound,because it is made up of Na and Cl atoms in a fixed ratio of 1:1
    2)   In the formation of the compound  NaCl, some amount of energy transformations took place and made this formation of NaCl.
      a permanent change ..... which means we cannot revert to the elemental state of Na and Cl from   NaCl  by any physical means.
      3)Example: the properties of Na and the properties of Cl are totally different than the properties of NaCl compound.

Other properties of a compound.

For example Na is a soft metal with grey colour and a metallic lustre and it is a solid , highly reactive  in presence of water( so its kept in kerosene always ), it can form an oxide as Na₂O.  when in presence of air and this oxide readily dissolves in water to form NaOH,....... but the salt has none of these properties.... the salt is crytalline , white in colour , dissolves readily in water but does  not form any base or alkali in water ,  is not so reactive in air or water  and has no metallic lustre.
The other element that forms NaCl is chlorine and that we know is a gas and is acidic ,,, it is also suffocating and acidic to moist  litmus.

Properties of compounds are thus not the same.....

But the salt is totally neutral and is not a gas but is a solid .In other words the compound has properties far different from the properties of any of the constituent elements.
 Further we cannot separate the constituent elements by any physical means.That is why we can differentiate between a compound and a mixture and study of compounds  becomes more interesting.