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4196 results in General and Classical Physics

Page 47 of 210

  • 11 - Energy Bands in Solids

  • Md Nazoor Khan, Simanchala Panigrahi
  • Book:
    Principles of Engineering Physics 2
    Published online:
    06 August 2018
    Print publication:
    08 August 2016, pp 406-428

  • Summary

    Introduction

    The behaviour of electrons and their energies in solids is related to the behaviour of all other particles around them where as their behavior in free space is completely different. The electrons in free space can posses any specified energy. The certain ranges of energies possessed by the electrons in a solid are called allowed energy bands and certain ranges of energies that can not be possessed by the electrons are called forbidden energy bands. The band theory accounts for many of the electrical and thermal properties of solids and gives the basic concepts behind the technological advancements of materials. The energy band theory of solids plays the most vital role in the development of semicondutor devices. The energy changes of electrons in solids interacting with photons of light, energetic electrons, x-rays and the like confirm the general validity of the band theory and provide detailed information about allowed and forbidden energy bands.

    Origin of Energy Bands

    The concepts of energy bands in solids can be accounted for by two different approaches; one is the classical approach and the other is the quantum mechanical approach.

    Origin of energy bands: The classical approach

    In the classical approach, the band of energies permitted in a solid is related to the discrete allowed energies – the energy levels of single, isolated atoms. According to the Bohr's atomic model, the energy level diagram of a hydrogen atom is depicted in Fig. 11.1, for three principal quantum numbers. As illustrated in the Fig. 11.1, an electron cannot have any energy between –13.6 eV and –3.4 eV. These are the energy levels of Bohr's hydrogen atom for principal quantum numbers 1 and 2 respectively.

    The energy is quantized. The range between –13.6 eV and –3.4 eV is the forbidden energy gap. Now we shall see what happens to these energy levels when a solid is formed due to the close aggregation of individual atoms.

    When two hydrogen atoms are brought together to form, the 1s energy level of two hydrogen atoms is split into two as shown in Fig. 11.2.

  • 1 - Crystal Structure

  • Md Nazoor Khan, Simanchala Panigrahi
  • Book:
    Principles of Engineering Physics 2
    Published online:
    06 August 2018
    Print publication:
    08 August 2016, pp 1-59

  • Summary

    Introduction

    Solids consist of atoms, molecules or ions packed very closely together. The forces that hold them in place give rise to distinctive properties of the various kinds of solid. In a broader sense, solids are classified into two categories: Crystalline and non-crystalline or amorphous. A crystal may be defined as a solid in which atoms, molecules or ions are arranged in a periodic pattern in three dimensions. That means crystals have a regular internal structure. An amorphous solid may be defined as a solid in which atoms or molecules are arranged arbitrarily in three dimensions, i.e., amorphous solids have no regular internal structure. A few examples of amorphous substances are glass, plastic, and gel, whereas the list of crystalline solids is very large; most metals are crystalline. Crystals that are composed of two elements are called binary crystals. There are thousands of binary crystals; some examples are sodium chloride (NaCl), alumina (Al2O3) and ice (H2O). A polycrystalline solid is made up of an aggregate of a large number of tiny single crystals called grains oriented in different directions and separated by well-defined boundaries called grain boundaries.

    Geometry of Crystals

    For the systematic study of crystals, we should first know the geometry of crystals in which actual atoms or molecules composing the crystal are ignored and their positions in space are taken into consideration. The positions of the atoms or molecules in the crystal define a set of points called point lattice. The point lattice may be regarded as the skeleton on which the actual crystal is built.

    Fundamental Terms

  • i. Point lattice The point lattice is defined as an array of points in space so arranged that every point has surroundings identical to that of every other point in the array. By identical surroundings we mean that, when we look in a particular direction putting ourselves at a lattice point, the same scenery is visible as that of any other point when we look in the same direction. A two-dimensional point lattice having infinite extension is shown in Fig. 1.1(a) and a three-dimensional point lattice assumed to have infinite extension is shown in Fig. 1.1(b). Point lattice, lattice or space lattice, are synonymously used.

  • 12 - Non-Destructive Testing

  • Md Nazoor Khan, Simanchala Panigrahi
  • Book:
    Principles of Engineering Physics 1
    Published online:
    06 August 2018
    Print publication:
    08 August 2016, pp 785-804

  • Summary

    Introduction

    The field of non-destructive testing (NDT) is a very broad area. It plays a critical role in assuring that structural components and systems perform their function in a reliable and cost effective fashion. NDT is a part of the quality control process. Non-destructive testing (NDT)/non-destructive inspection (NDI)/non-destructive evaluation (NDE) is a wide group of analysis techniques used in science and industry to detect surface or internal flaws of a material, component or system without causing damage. Since NDT does not permanently alter the article being inspected, it is a highly valuable method that can save both money and time in product evaluation, troubleshooting and research. NDT is not just a method for rejecting sub-standard materials; it is an assurance that the supposedly good is really good. NDT is a commonly used tool in forensic engineering, mechanical engineering, electrical engineering, civil engineering, systems engineering, aeronautical engineering, metallurgical engineering, electronic engineering, medicine, and art. In this chapter, we shall discuss the basic principle involved in NDT and very briefly, the methods of NDT.

    Objectives of NDT

    NDT provides an excellent balance between quality control and cost-effectiveness. There are NDE applications at almost any stage in the production or life cycle of a component.

    i. To assist in product development.

    ii. To screen or sort out incoming materials.

    iii. To assist in product development.

    iv. To monitor, improve or control manufacturing processes.

    v. To verify proper processing such as heat treatment.

    vi. To verify proper assembly.

    vii. To inspect in-service damage.

    NDE may be used to determine material properties such as fracture toughness, ductility, conductivity, and other physical characteristics. NDT are used in

    i. Flaw detection and evaluation.

    ii. Leak detection.

    iii. Location determination.

    iv. Dimensional measurements.

    v. Structure and microstructure characterization.

    vi. Estimation of mechanical and physical properties.

    vii. Stress/Strain and dynamic response measurements.

    viii. Material sorting and chemical composition determination.

    Methods of NDT

    The NDT technique uses a variety of scientific principles. The list of NDT methods that can be used to inspect components and make measurements is large and continues to grow. Researchers continue to find new ways of applying principles of physics and other scientific disciplines to develop better NDT methods. However, there are six NDT methods that are used most often.

  • 13 - Nano Structures and Thin Films

  • Md Nazoor Khan, Simanchala Panigrahi
  • Book:
    Principles of Engineering Physics 2
    Published online:
    06 August 2018
    Print publication:
    08 August 2016, pp 461-482

  • Summary

    Introduction

    The concept of nano structures and nano technology dates back to the history of the Nobel Laureate Richard Feynman's famous lecture in 1959 where he speculated the possibility of manoeuvring things atom by atom. He proudly said “There is plenty of room at the bottom”. By this sentence, he strongly pointed out that there is a lot of scope and application of materials at very small scale, i.e., at atomic or molecular level. Why cannot we write the entire 24 volumes of the Encyclopaedia Britannica on the head of a pin? One may wonder what it is so special at the nano scale? The answer to these questions is against the very notion that specific physical properties of a given material are the characteristic of the material itself and are irrespective of their size. This is no longer valid at the nano scale. There will be a drastic change in properties which are counter-intuitive and unbelievable. Yellow metal gold is no more yellow in any size or dimension. It may be purple red and orange. Cds under colloidal solution may yield a rainbow spectrum of colour. Ceramic oxides are not always brittle. Nanoceramics are ductile and malleable. What sounded as scientific fantasy or myth at that time, today has turned into reality.

    Nano science and technology cut across disciplines without boundary. For physicists and chemists, nano means in the range of dimension of a few atoms and molecules. For biologists, the visualization is to the dimension of the size of a DNA or to the scale of a cell. Scientists have now devised techniques to prepare tiny nano-particles which have peculiar properties. Nano technology is now a portal opening onto a new world. This chapter will provide the readers a brief look at: nano scale and its visualization, i.e., what nano is; nano science and nanotechnology, i.e., why one should care about nano; surface to volume ratio and quantum confinement, i.e., what makes nano so important; nano cluster and nano fabrication, i.e., how we prepare nano.

  • 9 - Dielectric Materials

  • Md Nazoor Khan, Simanchala Panigrahi
  • Book:
    Principles of Engineering Physics 2
    Published online:
    06 August 2018
    Print publication:
    08 August 2016, pp 289-353

  • Summary

    Introduction

    Dielectric materials are materials that do not conduct electricity, but can sustain an electric field. All dielectric materials are insulators. Insulators resist electric current when electric potential difference is applied. Dielectric materials can store electric energy. The molecules of a dielectric material are either polar or non-polar. Polar molecules are defined as molecules in which the centre of gravity of positive nuclei and negative electrons are not at the same point. Non-symmetrical molecules such as H2O, N2O and the like are polar molecules. Non-polar molecules are defined as molecules in which the centre of gravity of positive nuclei and negative electrons are at the same point. Symmetrical molecules such as H2, N2, O2 and the like are non-polar molecules.

    An Overview of Dielectric Polarization

    The phenomenon of slight relative shift of positive and negative electric charges in opposite directions within a dielectric, induced by an external stimuli like electric field, temperature, pressure etc is called dielectric polarization. Under the influence of an external applied electric field, non-polar molecules in dielectrics are polarized and become induced dipoles. This is depicted in Fig. 9.1.

    Under the influence of an externally applied electric field, the polar molecules in a dielectric [polar molecules are itself electric dipoles having inherent dipole moments] become aligned in the direction of the applied electric field. The stronger the applied electric field, the greater is the aligning effect. This is depicted in Fig. 9.2.

    The net effect of applying an electric field to either polar or non-polar dielectrics in the form of a slab is more or less the same. When an electric field is applied to a slab of dielectric in a direction perpendicular to one of its surfaces, negative charges are developed on one surface and positive charges developed on the opposite surface as shown in Fig. 9.3. Thus, the dielectric as a whole becomes polarized. These positive and negative charges are called induced charges as these charges are induced by applied electric field. These induced charges are not free but bound to the molecules lying just inside the surfaces.

Page 47 of 210