Imperfections in Solids

11 Key excerpts on "Imperfections in Solids"

• 

  eBook - PDF

  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  134 • WHY STUDY Imperfections in Solids? The properties of some materials are profoundly influ- enced by the presence of imperfections. Consequently, it is important to have knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials. For example, the mechanical properties of pure metals experience signifi- cant alterations when the metals are alloyed (i.e., when impurity atoms are added)—for example, brass (70% copper–30% zinc) is much harder and stronger than pure copper (Section 8.10). Also, integrated circuit microelectronic devices found in our computers, calculators, and home appliances function because of highly controlled concentrations of specific impurities that are incorporated into small, localized regions of semiconducting materials (Sections 12.11 and 12.15). Learning Objectives After studying this chapter, you should be able to do the following: 1. Describe both vacancy and self-interstitial crystalline defects. 2. Calculate the equilibrium number of vacancies in a material at some specified temperature, given the relevant constants. 3. Name and describe eight different ionic point defects that are found in ceramic compounds (including Schottky and Frenkel defects). 4. Name the two types of solid solutions and provide a brief written definition and/or schematic sketch of each. 5. Given the masses and atomic weights of two or more elements in a metal alloy, calculate the weight percent and atom percent for each element. 6. For each of edge, screw, and mixed dislocations: (a) describe and make a drawing of the dislocation, (b) note the location of the dislocation line, and (c) indicate the direction along which the dislocation line extends. 7. Describe the atomic structure within the vicinity of (a) a grain boundary and (b) a twin boundary. Thus far, it has been tacitly assumed that perfect order exists throughout crystalline materials on an atomic scale.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Metals and Materials

  Science, Processes, Applications

  • R. E. Smallman, R J Bishop(Authors)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 4 Defects in solids 4.1 Types of imperfection Real solids invariably contain structural discontinu-ities and localized regions of disorder. This hetero-geneity can exist on both microscopic and macroscopic scales, with defects or imperfections ranging in size from missing or misplaced atoms to features that are visible to the naked eye. The major-ity of materials used for engineering components and structures are made up from a large number of small interlocking grains or crystals. It is therefore immedi-ately appropriate to regard the grain boundary surfaces of such polycrystalline aggregates as a type of imperfection. Other relatively large defects, such as shrinkage pores, gas bubbles, inclusions of foreign matter and cracks, may be found dispersed through-out the grains of a metal or ceramic material. In general, however, these large-scale defects are very much influenced by the processing of the material and are less fundamental to the basic material. More attention will thus be given to the atomic-scale defects in materials. Within each grain, atoms are regularly arranged according to the basic crystal structure but a variety of imperfections, classified generally as crystal defects, may also occur. A schematic diagram of these basic defects is shown in Figure 4.1. These take the form of: • Point defects, such as vacant atomic sites (or simply vacancies) and interstitial atoms (or simply interstitials) where an atom sits in an interstice rather than a normal lattice site • Line defects, such as dislocations • Planar defects, such as stacking faults and twin boundaries • Volume defects, such as voids, gas bubbles and cavities. In the following sections this type of classification will be used to consider the defects which can occur in metallic and ceramic crystals. Glasses already (a) (b) V / / 1 / / (c) (d) Figure 4.1 (a) Vacancy-interstitial, (b) dislocation, (c) stacking fault, (d) void.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Materials Science and Engineering

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  Classification of crystalline imperfections is frequently made according to the geometry or dimensionality of the defect. Several different imperfections are discussed in this chapter, including point defects (those as- sociated with one or two atomic positions); linear (or one-dimensional) defects; and in- terfacial defects, or boundaries, which are two-dimensional. Impurities in solids are also discussed, because impurity atoms may exist as point defects. Finally, techniques for the microscopic examination of defects and the structure of materials are briefly described. imperfection point defect 4.1 INTRODUCTION The simplest of the point defects is a vacancy, or vacant lattice site, one normally oc- cupied but from which an atom is missing (Figure 4.1). All crystalline solids contain vacancies, and, in fact, it is not possible to create such a material that is free of these vacancy 4.2 VACANCIES AND SELF-INTERSTITIALS Point Defects WHY STUDY Imperfections in Solids? The properties of some materials are profoundly influenced by the presence of imperfections. Consequently, it is important to have a knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials. For example, the mechanical properties of pure metals experience significant alterations when the metals are alloyed (i.e., when impurity atoms are added)—for example, brass (70% copper–30% zinc) is much harder and stronger than pure copper (Section 7.9). Also, integrated-circuit microelectronic devices found in our computers, calculators, and home appliances function because of highly controlled concentrations of specific impurities that are incorporated into small, localized regions of semiconducting materials (Sections 18.11 and 18.15). • 93

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Callister's Materials Science and Engineering

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Classification of crystalline imperfections is frequently made according to the geometry or dimensionality of the defect. Several different imperfections are discussed in this chapter, including point defects (those as- sociated with one or two atomic positions); linear (or one-dimensional) defects; and in- terfacial defects, or boundaries, which are two-dimensional. Impurities in solids are also discussed, because impurity atoms may exist as point defects. Finally, techniques for the microscopic examination of defects and the structure of materials are briefly described. imperfection point defect 4.1 INTRODUCTION The simplest of the point defects is a vacancy, or vacant lattice site, one normally oc- cupied but from which an atom is missing (Figure 4.1). All crystalline solids contain vacancies, and, in fact, it is not possible to create such a material that is free of these vacancy 4.2 VACANCIES AND SELF-INTERSTITIALS Point Defects WHY STUDY Imperfections in Solids? The properties of some materials are profoundly influenced by the presence of imperfections. Consequently, it is important to have a knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials. For example, the mechanical properties of pure metals experience significant alterations when the metals are alloyed (i.e., when impurity atoms are added)—for example, brass (70% copper–30% zinc) is much harder and stronger than pure copper (Section 7.9). Also, integrated-circuit microelectronic devices found in our computers, calculators, and home appliances function because of highly controlled concentrations of specific impurities that are incorporated into small, localized regions of semiconducting materials (Sections 18.11 and 18.15). 98 •

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Materials Science and Engineering, P-eBK

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch, Aaron Blicblau, Kiara Bruggeman, Michael Cortie, John Long, Judy Hart, Ross Marceau, Ryan Mitchell, Reza Parvizi, David Rubin De Celis Leal, Steven Babaniaris, Subrat Das, Thomas Dorin, Ajay Mahato, Julius Orwa(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 4 Imperfections in Solids LEARNING OBJECTIVES After studying this chapter, you should be able to: 4.1 describe both vacancy and self‐interstitial crystalline defects 4.2 calculate the equilibrium number of vacancies in a material at some specifed temperature, given the relevant constants 4.3 name the two types of solid solutions and provide a brief written defnition and/or schematic sketch of each. 4.4 given the masses and atomic weights of two or more elements in a metal alloy, calculate the weight per cent and atom per cent for each element 4.5 for each of edge, screw, and mixed dislocations: (a) describe and make a drawing of the dislocation, (b) note the location of the dislocation line, and (c) indicate the direction along which the dislocation line extends 4.6 describe the atomic structure within the vicinity of (a) a grain boundary and (b) a twin boundary. WHY STUDY Imperfections in Solids? Properties of crystalline solids are determined by the type and arrangement of their atoms, and any alteration to this periodical pattern will be accompanied by a corresponding change in the material’s properties. While in some cases these imperfections may be undesirable, understanding their causes and effects allows scientists to control their presence adequately, and to produce advanced materials with tailored properties. (a) (b) Insulation Packaging Catalyst Substrate Stainless Steel Body Water Carbon Dioxide Nitrogen Tail Pipe Emissions: Hydrocarbons Carbon Monoxide Nitrogen Oxides Exhaust Gases: (c) (d) (a) Schematic diagram showing the location of the catalytic converter in an automobile’s exhaust system. (b) Schematic diagram of a catalytic converter. (c) Ceramic monolith on which the metallic catalyst substrate is deposited. (d) High‐resolution transmission electron micrograph that shows surface defects on single crystals of one material that is used in catalytic converters. Source: Figure (d) from W. J. Stark, L. Mädler, M. Maciejewski, S.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Advanced Electrical and Electronics Materials

  Processes and Applications

  • K. M. Gupta, Nishu Gupta, Ashutosh Tiwari(Authors)
  • 2015(Publication Date)
  • Wiley-Scrivener

    (Publisher)

  real crystals. They are of finite dimensions. They have broken bonds at the boundaries where bonding forces remain unbalanced. Thus the boundary of a crystal is a defect in itself.

  3.11.1 Disadvantageous Effects of Imperfections

  These imperfections lead to several deficiencies in the solids. Solids are generally imperfect. A perfect single crystal is rarely available. Polycrystalline solids are, inevitably, imperfect. We shall deal with all such imperfections (defects) of crystalline solids in this chapter.

  • Presence of imperfections in crystalline materials is generally undesired.
  • They decrease the mechanical strength of materials.
  • We have already discussed that a material does not attain its theoretical strength due to presence of imperfections.

  3.11.2 Advantageous Effect of Imperfection

  Imperfections affect structure-sensitive properties of crystals. Their presence is advantageous in certain applications.

  • Parts per million (ppm) doping of phosphorus in silicon changes the behaviour of intrinsic semiconductor and makes it suitable for various applications.

  3.12 Classification of Imperfections

  Imperfections in crystalline solids are classified as follows.

  S. No.	Main types	Sub-types
  1.	Point imperfections (zero-dimensional defects)	Vacancy, substitutional impurity, interstitial impurity, frenkel’s defect, schottky’s defect.
  2.	Line imperfections (1-dimensional defects)	Edge dislocation, screw dislocation, mixed dislocation.
  3.	Surface or planer imperfections (2-dimensional defects)	Grain boundary, twin or twinning, low angle boundary, high angle boundary, twist boundary, stacking fault, interphase.
  4.	Volume imperfections (3-dimensional defects)	Pores, foreign particle inclusions, non-compatibility regions, dissimilar natured regions.

  Point imperfections, line and surface imperfections may occur together in crystals. These defects are not visible to the naked eye. They can be visualized by using X-rays diffraction techniques and microscopes, already described in chapter 1. Imperfections are also classified on the basis of their dimensions, such as given below.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Physical Metallurgy

  Principles and Design

  • Gregory N. Haidemenopoulos(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  3

  Structural imperfections

  3.1 Introduction

  The main characteristic of crystal structure, discussed in the previous chapter, is the periodic arrangement of atoms. However, in a real metal, the crystal structure is not perfect and contains several types of imperfections, which disrupt the periodicity of the crystal. Structural imperfections have a strong influence on physical and mechanical properties of metals as well as on the evolution of phase transformations in metallic materials. Imperfections can be classified according to dimension:

  • Point defects, such as vacancies and interstitials
  • Linear imperfections, such as edge and screw dislocations
  • Surface imperfections, such as grain boundaries and interfaces
  • Three-dimensional defects, such as voids and inclusions

  All the above defects play a key role in the mechanical behavior of metals and the development of microstructure through phase transformations. For example, several phase transformations take place by atomic diffusion, where point defects, such as vacancies are essential. In addition, diffusion can be accelerated by the presence of dislocations or grain boundaries, which act as high diffusivity paths. The plastic deformation of metals takes place by dislocation glide, while strengthening is accomplished by impeding dislocation motion. The most common obstacles to dislocation glide are other dislocations, second phase particles or precipitates and grain boundaries. The three-dimensional imperfections, such as voids and inclusions, play a key role in the ductile fracture of metals. The examples discussed above, highlight the importance of imperfections in the behavior and properties of metals and alloys. The specific structural imperfections will be discussed in the following sections.

  3.2 Point Defects

  3.2.1 Vacancies and Interstitials

  In a perfect crystal all lattice sites are occupied by atoms. The two most important point imperfections or defects are, vacancies and interstitials, depicted in Figure 3.1

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Modern Physics

  The Quantum Physics of Atoms, Solids, and Nuclei: Third Edition

  • Robert L. Sproull, W. Andrew Phillips, W. Andrew Phillips(Authors)
  • 2015(Publication Date)
  • Dover Publications

    (Publisher)

  9         

  Imperfections in Solids

  9-1 INTRODUCTION

  Some properties of solids are practically the same for perfect crystals as for crystals with small concentrations of chemical impurities or with other deviations from perfection. Examples of such properties are density, heat capacity, and thermal expansion. On the other hand, minute deviations from crystal perfection control many of the properties of solids, such as the strength of metals and the electrical conductivity of semiconductors, and cause interesting phenomena, such as the light emission by insulators. In this chapter we study a few examples of the ways in which imperfections determine the behavior of solids. The analysis in Chapters 7 and 8 provided the basic understanding required to investigate these and many additional imperfection phenomena.

  Section 9-2 surveys the types of imperfections present in solids. Diffusion is described briefly in Sec. 9-3 . The absorption of light in insulating crystals is considered in Sec. 9-4 , and the change in electrical conductivity produced by this absorption of light is studied in Sec. 9-5 . The emission of light by solids is considered in Sec. 9-6 . The effect of dislocations on the mechanical properties of metals and alloys will be treated in Sec. 9-7 . The physics of solid surfaces is discussed in Sec. 9-8 . The electrical conductivity of semiconductors, another important application of imperfection theory, will be considered in detail in Chapter 10 .

  9-2 TYPES OF IMPERFECTIONS

  In a perfect crystal every atom is in precisely the correct place in the crystal lattice, there are no atoms missing from sites in the lattice, and there are no foreign atoms. Furthermore, if the perfect solid is not a metal, each of the energy bands is either completely empty (no electrons) or completely full

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Solid State Materials Chemistry

  • Patrick M. Woodward, Pavel Karen, John S. O. Evans, Thomas Vogt(Authors)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  2 Defects and More Complex Structures We have seen in Chapter 1 that the solid state world is dominated by long-range order and beauty. Crystalline materials contain highly symmetric arrangements of atoms that are regularly repeated over millions of unit cells. In this chapter, we will question how realistic this picture is. In reality, there are a number of ways in which crystalline materials deviate from perfect long-range order and contain imperfections or disorder. This can occur via “mistakes” in the atomic arrangement of a pure material or via the introduction of impurity atoms giving rise to chemical disorder. These defects can occur locally or extend over lines, planes, or 3D volumes of materials. Such effects, even when they occur at very low levels, are vitally important to the chemical and physical properties of materials. They turn low-value minerals into precious gemstones; soft iron into strong and corrosion-resistant stainless steel; and they control the semiconducting properties of silicon in the transistors powering modern electronics. This chapter also introduces a variety of ways in which materials can deviate from having simple stoichiometric formulae. This can occur either via the presence of defects or chemical substitutions in a material or can have a variety of more complex structural origins. In later chapters, we will see how these various effects influence many of the important properties of functional materials. 2.1 Point Defects in Crystalline Elemental Solids We have seen that the structures of many elements can be described in terms of regular arrays of spherical atoms. At the local level, this order can be perturbed by three different types of point defects; vacancies, interstitials, and substitutional disorder. These are shown schemat- ically in Figure 2.1. A vacancy occurs when an atom is missing from a site in the structure as shown in Figure 2.1, left.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  Surface defects represented schematically in Figure 6.16 are noted on the crystals. [From W. J. Stark, L. Mädler, M. Maciejewski, S. E. Pratsinis, and A. Baiker, “Flame-Synthesis of Nanocrystalline Ceria/Zirconia: Effect of Carrier Liquid,” Chem. Comm., 588–589 (2003). Reproduced by permission of The Royal Society of Chemistry.] 226  Chapter 6 Imperfections in Solids reside. An explanation of the variety of textural contrasts in this photomicrograph is provided in Section 6.12. Miscellaneous Interfacial Defects Other possible interfacial defects include stacking faults and ferromagnetic domain walls. Stacking faults are found in FCC metals when there is an interruption in the ABCABCABC . . . stacking sequence of close-packed planes (Section 3.16). For fer- romagnetic and ferrimagnetic materials, the boundary that separates regions having different directions of magnetization is termed a domain wall, which is discussed in Section 18.7. With regard to polymeric materials, the surfaces of chain-folded layers (Figure 4.13) are considered to be interfacial defects, as are boundaries between two adjacent crystal- line regions. Associated with each of the defects discussed in this section is an interfacial energy, the magnitude of which depends on boundary type, and which varies from material to material. Normally, the interfacial energy is greatest for external surfaces and least for domain walls. Tutorial Video: Differences among Point, Linear, and Interfacial Defects Every atom in a solid material is vibrating very rapidly about its lattice position within the crystal. In a sense, these atomic vibrations may be thought of as imperfections or de- fects. At any instant of time not all atoms vibrate at the same frequency and amplitude or with the same energy. At a given temperature, there exists a distribution of energies for the constituent atoms about an average energy. Over time, the vibrational energy of any specific atom also varies in a random manner.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  The Science and Engineering of Materials, Enhanced, SI Edition

  • Donald Askeland, Wendelin Wright, Donald Askeland(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Surface defects Imperfections, such as grain boundaries, that form a two-dimensional plane within the crystal. Thermal grooving A technique used for observing microstructures in ceramic materials that involves heating a polished sample to a temperature slightly below the sintering temperature for a short time. Tilt boundary A small angle grain boundary formed by edge dislocations. Twin boundary A surface defect across which there is a mirror image misorientation of the crystal structure. Twist boundary A small angle grain boundary formed by screw dislocations Vacancy An atom or an ion missing from its regular crystallographic site. Yield strength The level of stress above which a material begins to show permanent deformation. Problems Section 4-1 Point Defects 4-1 Gold has 5.82 3 10 8 vacancies/cm 3 at equi- librium at 300 K. What fraction of the atomic sites is vacant at 600 K? 4-2 Calculate the number of vacancies per m 3 for gold at 900°C. The energy for vacancy formation is 0.93 eV/atom. 4-3 Calculate the number of vacancies per cm 3 expected in copper at 1080°C (just below the melting temperature). The energy for vacancy formation is 83,680 J/mol. 4-4 The fraction of lattice points occupied by vacancies in solid aluminum at 660°C is 10 –3 . What is the energy required to create vacancies in aluminum? 4-5 The density of a sample of FCC palladium is 1980 kg/m 3 , and its lattice parameter is 0.38902 nm. Calculate (a) the fraction of the lattice points that contain vacancies; and (b) the total number of vacancies in a cubic centimeter of Pd. 4-6 The density of a sample of HCP beryllium is 1844 kg/m 3 , and the lattice parameters are a 0 5 0.22858 nm and c 0 5 0.35842 nm. Calculate (a) the fraction of the lattice points that contain vacancies; and (b) the total number of vacancies in a cubic centimeter of Be. 4-7 BCC lithium has a lattice parameter of 0.3508 nm and contains one vacancy per 200 unit cells.

  Sign up to read

  Learn more about book