21 Application of electrons in the study of defects and homogeneity of crystals

Prof. P. N. Kotru

21.  Application of electrons in the study of defects and homogeneity of crystals

21.1 Light is a wave motion and one can use it for looking at objects which are larger as compared to wavelength of light , which is of the order of 10─4cm. Radiation having a shorter wavelength viz., x-rays are used to determine the internal structure of a crystal. In the study of internal arrangement of atoms in a crystalline solid, resolving power is extremely important. The resolving power which is defined as the smallest distance say x , between any two adjacent objects which an optical instrument is capable of distinguishing as different objects , is of the same order of magnitude as the wavelength of the light that is used in making observation. The formula for resolving power is given as:

X =   λ /2µsinα, Where λ is the wavelength of the radiation used,

µ is the refractive index of the medium between the objective lens and the object and half the angle subtended by the objective lens at the object under observation. 

To increase x, it is required to increase the value of µ and α and have λ as small as possible. In optical microscopes, oil immersion objectives are provided on which a drop of special oil is used between specimen and the objective to increase µ. There are optical microscopes which are provided with special type of objectives known as ‘oil immersion objectives’ for this purpose. However, µ and α cannot be beyond a particular limit. The solution, therefore, lies in using radiation of smaller wavelength. Electrons provide a solution to this problem. If electrons are accelerated through a potential difference of 200 volts, they have a wavelength of nearly 1Å which is much smaller as compared to wavelength of visible light. It is electron microscope where electrons are used as a probing radiation, thus providing a superior resolving power which is used to examine the shapes and sizes of crystals at a much finer level.

One of the most useful capabilities of the electron microscope is that it forms electron diffraction patterns from very small regions of a sample which may be typically about 1µm in diameter. Combination of the results of electron diffraction from a substance and morphological evidence from electron micrographs of the same region provides invaluable information in relating, for example, growth habits to crystal structure features and in studying epitaxial relationships between crystalline phases.

21.2 Electron Microscope: Basic Operating Principles.

The field of electron microscopy has advanced immensely over the years and its application to x -ray microanalysis, element mapping, nanoscience, materials science, forensic science, solid state electronics, geosciences, minerals and metallurgy is ever expanding. However, we shall consider here the physical features common to most electron microscopes. Figure 21.1 is a schematic diagram which shows course of rays for an electron microscope having three electromagnetic lenses.

Figure 21.1: Ray diagram of an electron microscope

The electron microscope has a column which is maintained at a pressure of about 10─4torr. The column has four principal sections. At the top there is an electron gun comprised of heated filament and grid at a potential of 100 KV (or so) negative with respect to earth and a system of two electromagnetic lenses form a double condenser system which provides a focussed beam of electrons at the sample holder. The sample is held on a support in the line of electron beam. The sample is provided with an arrangement for translational movements in the plane of the sample and also rotational movements about two mutually perpendicular axes lying in the plane of the sample. After passing through the sample, the electrons enter the enlargement section. This section usually has atleast three electromagnetic lenses to focus and enlarge the images generated by transmission of the electron beam through the sample. In the final stage, the beam enters the detection area which is provided with a fluorescent screen for direct viewing and a camera for taking a permanent record. All these sections are shown in the schematic diagram of figure 21.1. The final image is called electron micrograph which shows a small part of the sample magnified to 2×104 or more. Modern electron microscopes have a resolution of 10Å quite readily, and 2.5─3Å resolution can be achieved by careful preparation of sample and accurate alignment of the electron optics.

21.2.1    Preparation of sample

The sample used in electron microscopy is in the form of either thin section of the material concerned, or a fine powder supported on a carbon film or a thin plastic. The thickness of the sample is required to be such that the electron beam penetrates through it. However, the exact thickness of the sample is decided by the atomic weight of the sample element. It is typically about 0.5 µm thick if an electron microscope operates at voltage of 200 KV. In any case, the thin samples are supported on a 2.3 or 3.05 mm diameter suitable grid. The grid is then mounted in the sample holder of the electron microscope.

Studies on surface morphologies of massive samples are made by replication technique which involves deposition and subsequent removal of thin carbon or plastic films onto the surface, so that they replicate the shape of the surface for investigations.

Scanning electron microscopy provides better surface data. If the sample is a nonconductor, the surface is required to be coated with a thin layer of a conducting medium. Operation of the electron microscope has to be under a vacuum of better than 10─4torr so as to reduce scattering and absorption of electrons by gas molecules.

21.3  Diffraction of electrons.

Electron diffraction provides a very valuable tool which has the potential of deriving information regarding crystallography of materials. It is well known that an electron of mass m moving with a velocity v is associated with a wavelength λ given by: λ = h/p = h/mv , ……………21.1

where h is Planck’s constant.

An electron accelerated through a potential of around 100 KV has a wave form with wave length in

angstroms given by:   λ =12.27 V ½(1 + 0.978 x 10─6 V) ─1/2,

where V is the accelerating potential in volts.

On account of the wave nature of electrons, they are diffracted by crystalline material in a similar way as x-rays get diffracted. However, there is a difference between x-rays and electron diffraction. Electrons are associated with very short wavelength of nearly 0.037Å for 100 KV electrons .The electron beam can be focussed and data from areas < 1µm diameter obtained. These advantages of using electrons as probing particles make electron diffraction a better tool for investigations on small crystals than are x-rays. As for example, very low Bragg angles at which diffraction takes place , the 2θ angle being less than 5⁰ for d – spacings> 0.5Å, enables to get good undistorted representations of the reciprocal lattice directly on a flat plate camera. The same would involve a complicated mechanism if one uses x -rays such as in the use of precession camera.

Diffraction of electrons by crystalline solids involves a mechanism which is different from that of x-rays. The mechanism is different primarily on account of higher energy of electrons. The diffraction of x – rays is due to their interaction with the electron clouds surrounding the atoms present in the matter. As against this, the electrons interact not only with the nuclei of the atoms but also the electron clouds.

Electrons generally are more strongly scattered than are x-rays, which creates more complications because of rediffraction of already diffracted beams. The double diffraction of electrons creates uncertainty in the measurement of intensities of electron diffraction reflexion because of which it is not used for the determination of structure.

Generally, it is a practice to restrict the area of the specimen to be investigated and contributed to the diffraction which is achieved by inserting a ‘selected area aperture’ called as selected area electron diffraction (abbreviated as SAED or SAD ). It is in the form of an earthed plate with an aperture of about 50 µm, in the plane of the first image, at FI1 in figure 21.1. In this manner the diffraction pattern involves an area which is effectively limited to a radius of about 1µm diameter around the primary axis.

Larger apertures are also used for some type of studies. Larger apertures lead to composite patterns from many crystals which form powder rings in case of such a material that is polycrystalline with random orientation. It is known as ‘General Area Diffraction’ and these studies are of interest in texture and preferred orientations, in materials like platy minerals such as clays.

‘Selected area electron diffraction’ is important in order to make use of transmission electron microscopy. The facility of SAED enables it to obtain both a visual image and an electron diffraction pattern from the same small volume of the specimen which typically may be of the order of 1µm in diameter.

21.4  Electron Diffraction Patterns

The electron diffraction pattern from a given material may be produced by the following : i) Single crystal in the material or,

ii) Random polycrystalline aggregate (in case of large selected area) or, iii) Polycrystalline aggregate

exhibiting preferred orientation.

In case it is due to single crystal, the pattern is in the form of a series of regularly spaced spots corresponding to a section of the reciprocal lattice of the crystal. For a random polycrystalline aggregate the pattern consists of a series of circular rings as it happens to be in the case of x-ray powder pattern. The pattern due to polycrystalline aggregate with preferred orientation is in the form of a series of rings with superimposed intensity maxima corresponding to the texture of the material.

Let us take up powder diffraction and single crystal pattern in a slightly more detail.

21.4.1 Powder Diffraction Patterns

Diffraction of electrons by the lattice of a crystal is the same as that of x-rays, though there are differences in their mechanism as said above. The positions of the maxima for the cones of diffracted radiation from a powdered sample are given according to Bragg equation: λ = 2dsinθ,

The wavelength of electrons is very small which restricts 2θ to a maximum value of about 5⁰. Because of the low value of θ, one can make an approximation that sin θ = θ in radians. Taking the diameter of the powder ring as measured on the photographic plate to be 2R and L as the effective camera length ( or the effective distance from specimen to camera after allowing for the magnification M) , one can show on application of simple geometry that

R = L tan 2θ

Considering 2θ to be small, tan 2θ is replaced by 2θ, so that

Now, λ = 2 d .θ

R = L. 2θ,

(replacing sin θ by θ in Bragg equation), Or,

θ  = λ/2d.

Substituting for θ in the above equation:

R = L . 2λ/2d = L . λ/d, Therefore,

d = λ L/R

The factor λL is called as “ camera Constant “ which is determined experimentally by taking a standard material such as aluminium or gold or thallous chloride in order to calibrate the instrument. The set of d-spacings and intensities are used in conjunction with the JCPS file and indexes in order to identify crystalline phases.

Simple powder electron diffraction data does provide some information regarding structure of simple structures, particularly that of cubic class. However, the information gets limited for more complicated structures as is the case with most minerals.

21.4.2    Single Crystal Diffraction Patterns

Since in electron diffraction, electrons are the probing radiations which are associated with very short wavelengths, Ewald sphere and the reciprocal lattice construction are of particular use in interpreting single crystal electron diffraction patterns. The radius of Ewald’s sphere is taken to be equal to 1/λ . Since very small wavelengths are associated here because of involvement of electrons, the radius of Ewald sphere is made very large, so large that the section of it (Ewald sphere) in generating the electron diffraction pattern is effectively planar. As a result of this its intersection with the reciprocal lattice occurs virtually in a single plane without the marked curvature encountered with x-rays. The magnified image produced on the photographic plate is, therefore, a virtually undistorted projection of the reciprocal lattice as it appears to the electron beam.

Single crystal diffraction patterns may provide data other than simple unit cell parameters. In principle, the data in the pattern could be used to determine the space group of the unknown crystal.

21.5      Role of electron beam in chemical analysis

Electron beam is also used as the excitation radiation for chemical analysis of micro– sized volumes. The technique of ‘microanalysis’ has also become very effective in analysing and interpreting deviations from normal surface of a crystal. A surface microtopographical investigation aided by microanalysis has contributed a great deal in the understanding of crystal growth. The combination of elemental analysis with surface microscopy using scanning electron microscopy is especially very important in enabling the composition of a phase to be related to the microstructures exhibited by a crystal.

21.5.1     Background of Microanalysis

Figure 21.2: Schematic diagram revealing the energy distribution of electrons emitted from a surface on using incident primary beam of electrons of energy Ep=2keV

Figure 21.3: Schematic representation of energy diagram revealing transitions involved in the excitation of (a) characteristic x-ray emission (b) Auger electron emission

The technique of microanalysis involves detection and analysis of some kind of electromagnetic radiation emitted from the material on excitation. The excitation may be induced by electrons, or by x-rays or by ions. Here, we are concerned with electrons as radiation for excitation. The two instruments involved in a major way include scanning electron microscope (SEM) and the electron probe microanalyzer (EPMA). Both these instruments use electrons for scanning the specimen surface.

Excitation by electrons may be described by considering the energy distribution of the electrons which get emitted from a metal surface when the primary beam of energy 2KeV is incident on it. The spectrum of electron emission will be as follows:

i) Some portion of the electrons gets elastically scattered. That means this portion of electrons get scattered without any loss of energy and so such electrons result into an elastic peak at an energy which is equal to the incident primary beam energy Ep = 2 KeV. Detection of these electrons are used to provide structural information about the material under study. Actually, these are the electrons which have undergone Bragg diffraction and so form the basis of the technique of low energy electron diffraction, popularly known as LEED. The LEED provides structural and crystallographic information about the atom positions in the first layers of the crystal sample which is required to be in the form of single crystal.

ii)  Below the elastic peak there are some smaller peaks due to those diffracted primary  electrons which have suffered energy losses on account of Plasmon interactions. iii) Next are the back– scattered primary electrons which are scattered inelastically. As shown  in the schematic diagram of figure 21.2, the back-scattered electrons form the general continuous spectrum of energies range downward from the incident primary beam of electrons of energy Ep.

iv)  On the lower side of this energy range is a secondary electron peak. These are the electrons                   which were originally present in the solid but have been emitted as a result of ionisation of the atoms in the solid due to inelastic scattering of the primary beam. Practically, it is not possible to make distinction between low energy back-scattered primary electrons (inelastic) and the true secondary electrons. The true secondary electrons are conventionally taken as those which have an energy of less than 50 eV. It is these two types of radiation, i.e., the back-scattered and the secondary emitted electrons which are used in the image formation by the scanning electron microscope.

v) The above said electrons form the radiation emitted from the solid. However, these electrons are only a part of the total radiation emitted from the solid. Figure 21.3 describes schematically the ionisation process as said above. In case the incident electron beam has intrinsic energy beyond a certain limit, it may displace an electron from one of the inner electron shells of an atom in the solid say the K -shell. This limit of energy, however, depends on the material under investigation. The situation is so created is energetically unstable because of which an electron from a higher level, say L2, may fall into the vacant position resulting into releasing an energy

∆E = Ek─ EL2 ,

which could appear in the following ways:

1. Emission of characteristic x-ray.

The transition may take place so as to emit photon of electromagnetic radiation of frequency ν; ∆E= hν as shown in figure 21.3 (a). So, for the transition EL2 → EK, the emission of characteristic Kα1 x-radiation takes place. These x-rays, being characteristic of the material, can be used for identification and analysis. SEM and EPMA uses this emission for analysis.

It may also happen that a photon of ultra–violet or of visible light may be emitted either in place of x-ray photon or in combination with the x-ray photon. This phenomenon is known as cathodoluminescence which is also used in image formation by the SEM.

2.  Auger electron emission.

Following the L2→ K electronic transition the energy may be transferred to yet another electron in the L3 level , which is then released as an Auger electron as shown in figure 21.3 (b); the electron involved in this process is referred to as KL2L3 Auger electron which carries energy equal to ( Ek ─ EL2 ─ EL3 ). It is again characteristic of the atom from which it is released and as such these electrons could be used for identification and analysis. Figure 21.2 shows the auger electrons as small peaks in the electron distribution system and are used as surface and near–surface techniques. This field is known as Auger electron spectroscopy which is used effectively as microanalytic technique for surface analysis.

21.6  The Scanning Electron Microscope

The study of solids by using the technique of scanning electron microscopy started somewhere half a century back. Essential parts of a scanning electron microscope may be described by referring to figure 21.4.

Figure 21.4: Block diagram of scanning electron microscope showing its essential parts

It has already been explained that the specimen to be studied with the help of TEM is required to be in the form of a very thin section enabling it to be studied in transmission.

For SEM the specimen is generally opaque which is studied in back reflection.

In the TEM the incident beam of electrons after interacting with specimen during its passage through it, is focussed by a system of lenses to form the magnified image. However, in the SEM, the lens is designed so as to focus the incident beam of electrons to a fine spot, around 100 to 300 Å diameter which then interacts with the specimen. This fine spot is dynamically scanned across a square area of the specimen surface. The interaction leads to scattering of electrons from the surface. The scattered electrons are received by the Faraday cage which appears in the form of a signal. The signal is got amplified. The amplified signal is used for modulation of the brightness of a cathode ray tube display. This modulated signal is scanned synchronously with the incident beam of electrons so as to obtain one-to-one image of the specimen surface. The magnification in this case is given by the ratio of the area of the cathode ray display tube to the area of the scanned specimen surface. While the area of the cathode ray display tube is constant for the instrument, the area of the scanned specimen surface is variable and depends on how much area is under scanner. The latter area can be varied between 20 X to 100,000 X.

The resolution of the instrument depends on the size of the spot used. However, one cannot reduce the spot size beyond a particular limit. The optimum resolution that has been attained falls in the range 100-200 Å. This resolution is poor as compared to the resolution attainable in the case of TEM which at best is in the range 2-5 Å. Routinely operated TEM provides a resolution somewhere in the range 10-50 Å. Comparing this resolution that is attainable with optical microscope, it is at least ten times better.

21.7 Applications

The depth of field of the optical microscope is of the order of 1000 Å. It means that the surface under investigation is required to be flat to within limit in order to have the whole image in focus. Depth of field in the SEM is one thousand times greater or about 0.1 mm or 106 Å. Looking at the image even at high magnification of 104 X, the depth of field of the SEM is about 1µm. This makes the use of SEM advantageous for microtopographical studies on specimen surfaces.

It is possible to have almost the same depths of field with the TEM. However, one has to use replication technique in order to be able to make surface microtopographical examination of crystal surfaces.

21.7.1 Modes of operation.

 The principal modes of operation are the following: emissive mode,

a) The

b) The reflective mode,

c) The absorptive mode,

d) The cathodoluminescent mode,

e) The x-ray mode.

Let us describe these modes of operation very briefly.

21.7.1.1  Emissive mode .

In this mode of operation, the electron collector is positively biased in order to capture the low energy secondary electrons from the specimen material, besides the primary back-scattered electrons. Secondary electrons originate from within 50 Å of the surface of material specimen. So, the information provided by these secondary electrons is characteristic of the actual surface. It is possible to obtain optimum resolution with this mode.

21.7.1.2   Reflective mode.

In the reflective mode, the collector is slightly negatively charged. It is done so that only high energy back-scattered primary beam of electrons get detected while others are prevented from detection. In fact, the back-scattered electrons originate from the material within a few microns of the surface of specimen and their intensity is dependent on the atomic number of the elements that compose the surface.

21.7.1.3   Absorptive mode.

In this mode, the electrical lead is attached to the specimen. The current that flows in it acts as the signal to the cathode ray display. For any particular region of the specimen surface, the more secondary electrons are generated, or the more primary back-scattered electrons are produced, the smaller is the current generated in the specimen because of which the signal in the attached lead is reduced and so the display screen gets darker.

One, therefore, finds that the display in this mode is complementary to those obtained in the emissive or the reflective modes.

21.7.1.4   The cathodoluminescent mode .

Certain solids exhibit fluorescence when excited by electrons. When the SEM is used in the luminescent mode, the electron collector system is replaced by photomultiplier tube and light guide. The output from this unit is again used to modulate the cathode ray display.

21.7.1.5   The x-ray mode.

In this mode, the image formation is due to x-rays generated from near the surface. The x-rays thus generated are characteristic of the elements present in the specimen surface and so provide information regarding elemental distributions across the area of the specimen scanned. The x-rays may be detected either on the basis of their wavelengths or their energies. In the former case dispersive method using a crystal spectrometer is used. However, in case of the latter, non-dispersive mode using energy sensitive detection system is employed. On the basis of this, the nomenclature used is “Energy Dispersive Analysis of X-rays (EDAX)”.

Figure 21.5: Some basic modes of operation in scanning electron microscopy

Figure 21.5 is the block diagram showing the arrangement for SEM set-up in various modes of operation as specified above. So, the SEM can be used to study specimen surfaces using any of these modes. SEM can provide information on four main aspects concerning solid materials .Firstly, in the study of surface microtopography, exploiting its advantage of having excellent depth of field.

Secondly, bulk microstructure may be investigated by using different modes of imaging. For example, minor surface features may be identified, using the high resolution that is obtainable in the emissive mode and correlated with the improved “atomic number” contrast which is obtainable using the reflective or the absorptive modes, to address and determine regions of different chemical composition. X-ray studies may then have to be conducted to identify the elements on definitive basis. Cathodoluminescence may then be used to reveal presence of some constituents which may occur as trace impurities.

Thirdly, back-scattered electrons can be used to determine relative concentration of each element present. However, better estimate of the concentration of each element can be made using characteristic x-rays.

Finally, it is possible to have information regarding crystallography of single crystal specimens by varying the incident beam angle at a given spot.

21.8  The Electron Probe Microanalyzer (EPMA).

The basic purpose of EPMA is primarily to provide quantitative chemical analyses whereas the image formation is of secondary interest. In SEM, the situation is reversed because the primary aim is to provide image formation whereas quantitative chemical analysis is of secondary concern. However, both these instruments are competent enough to provide complementary information to advance our

understanding of the material under investigation. The designing of SEM and EPMA is very similar. The EPMA consists of an evacuated column containing an electron gun, electron lenses and deflection coils to scan the beam across the specimen. Electron and X-ray detectors are positioned close to the specimen surface so that the angle of the emitted x-rays is about 70⁰ to reduce absorption effects on account of surface irregularity to minimum. Since the EPMA is required to have high sensitivity for x-ray detection, the primary electron beam is incident normally on the surface of the specimen. The x -rays are excited for a depth of about 1µm in the material sample, and the minimum volume that can be analysed is of the order of a cubic micron.

The characteristic x-rays having been generated by an electron beam, are primary xrays and so they are superimposed on a continuous background, from which they are required to be selected before measurements. The x-ray wavelength is characteristic of the element involved and the observed intensity is proportional to its concentration.

The x-ray wavelengths are initially sampled with the help of a crystal spectrometer so as to select the wavelength that is required for transmission to the x-ray detector. In order to examine the elements of atomic number falling in the range 4 to 92, range of wavelengths between 100 Å to 0.5 Å are required. The heavier elements are usually detected through their L-series x-radiations.

The output channels on the EPMA include:

i)  Light optical system required for directly viewing the material specimen. This may include a

cathodoluminescence unit.

ii) Electron optical system for producing either a secondary or a back-scattered electron image, as in the

SEM, on the cathode ray tube.

iii) X-ray identification system which provides a direct image, with positive contrast at those

sites containing the element for which the spectrometer is set. iv) X-ray intensity measurement system

which provides quantitative information for analysis through a Pen recorder, tape punch and printout

device.

The primary aim of EPMA is analysis but it is also important to image the region which is under analysis.

This is achieved by optical, electron or x-ray imaging.

In qualitative analysis work, the x-ray spectrometer is set to the wavelength corresponding to the species of interest, and the resulting x-ray image generated on the cathode ray display gives the distribution of that element over the area being scanned. It is difficult to analyse light elements. As atomic number of an element decreases, the wavelength of characteristic x-rays becomes longer. This difficulty is felt particularly for elements with

Z ≤ 10. So, for elements like fluorine, oxygen, nitrogen, carbon, boron and beryllium with Z varying between 9 and 4, their Kα wavelengths increase in order 18, 24,32,44,68 and 113 Å respectively. However, this problem has been solved to some extent by using special heavy metal stearate crystals in the spectrometer.

EPMA has proved to be of great use in the field of crystallography, mineralogy, metallurgy and materials science. It has made important contribution to an understanding of materials, so far as their physical and chemical perfection is concerned. Its ability to perform analysis on a very fine scale makes it to be a valuable tool because it may be impossible physically to separate the phases in order to carry out a standard chemical analysis.

Mineral identification is one of its major applications. It has been acknowledged by naming one new mineral after the name of the person first responsible for the development of the electron probe microanalyzer (R. Castaing, 1951, Ph.D. Thesis, University of Paris, Publ. O.N.E.R.A. No. 55). The mineral is known by the name Castaingite and the person who has contributed to its development is R.Castaing.

Besides identification, EPMA can provide accurate compositional analyses leading to the study of solid solutions and of phase equilibria,

Cathodoluminescence, as in the SEM, provides information regarding presence of certain trace elements, such as rare earths which can be detected at concentration s much below that of the normal detection capability of the EPMA.

The SEM and the EPMA are the two most versatile techniques, be it qualitative or quantitative analyses.

21.9 Surface & Near – Surface Techniques.

In the past half a century a number of instruments have been developed which push the depth resolution down to include the surface layers of atoms only , thus contributing towards information regarding surfaces of the material specimen . Thus they are the microanalytical techniques, at least in one dimension.

These techniques are:

1. Auger Electron Spectroscopy (AES)
2. Low Energy Electron Diffraction (LEED)
3. Electron Spectroscopy for Chemical Analysis (ESCA)

Important application of AES lies in the field of studying surface composition. LEED provides structural and crystallographic information about the atom positions in the first few layers of the material specimen, provided the sample is in the form of a single crystal. ESCA is used to distinguish between different binding or oxidation states. Detailed discussion of these techniques is beyond the scope of the subject at hand.

The entire discussions on exploitation of electrons in various techniques, especially TEM/SEM/EPMA/AES/LEED/ESCA have been supplementary and complimentary to one another, combining to provide the following broad spectrum of information: i) Elemental analysis,

1. ii) Microstructural information and revelation of the distribution of the various phases, iii) Crystallographic information, providing information on crystal structure.

The SEM and the EPMA are the two most versatile techniques, depending on whether quantitative or qualitative analyses are required. These techniques provide information on physical and chemical perfection of the material, besides different types of information regarding other crystallographic aspects of the material specimen.

References.

1. Cracknell,A.P. “ Crystals and Their Structures”,Pergamon Press,London,1969.
2. Nicol,A.W. “ Physicochemical Methods of Mineral Analysis”,Plenum Press,N.Y.,1975.
3. Franks,A. “ Applied X-Rays,Electrons& Ions” (ed.by Agarwala,B.K.),NPL Manographs on Science and Technology”,NPLPublication,N.Delhi.

Suggested Reading For More Information On Instrumentation,Operational

Techniques & Other Related Details.

1. Cosslett,V.E.” Electron Microscope”,Sigma,London.
2. Cosslett,V.E. “ Electron Optics”,Univ.Press,Oxford.
3. Klemperer,O.” Electron Optics”, Univ.Press, Cambridge.