Interstitial Defect

10 Key excerpts on "Interstitial Defect"

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  Materials Analysis by Ion Channeling

  Submicron Crystallography

  • Leonard C. Feldman, James W. Mayer, Steward T.A. Picraux(Authors)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  On the other hand, if defects trap embrittling species, their flow and accumulation at grain boundaries or other failure points may be impeded. 193 194 9. IMPURITY-DEFECT INTERACTIONS In most materials, vacancies, interstitials, and their clusters can inter-act strongly with impurities. The influence of vacancies and interstitials can be distinguished by their temperature of migration. Their interactions with impurities can be monitored with channeling when the interaction results in a displacement of the impurity from normal lattice sites. In metals, interstitials generally have a lower activation energy of motion than do vacancies, so that appreciable migration of interstitials can occur at temperatures where vacancies are essentially immobile. For example, in Al, resistivity and positron annihilation measurements show free inter-stitials migrate at =45 Κ and vacancies at =200 K. In this chapter we discuss three different categories of defect interac-tions in metal crystals: (1) irradiation of substitutional alloys to study metal-solute interactions with vacancies and interstitials, (2) interstitial gas atom interactions with point defects, and (3) defect accumulation during channeling analysis. Defect-impurity interactions can be studied since controlled numbers of interstitials and vacancies can be introduced by light ion irradiation, and solutes or impurities can be introduced into the sample by alloying, diffusion, or ion implantation. 9.2 Metal-Solute Interactions with Interstitials and Vacancies Solute atoms in metal crystals can trap mobile defects. The size of the solute atom is one factor in determining the type of defect that is trapped. In general, small solute atoms trap interstitials of the host lattice, whereas large solute atoms trap host lattice vacancies, thereby minimizing the strain energy in the crystal.

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  Atomic Mechanics of Solids

  • A.K. Macpherson(Author)
  • 2012(Publication Date)
  • North Holland

    (Publisher)

  A l t h o u g h it is clear that defects have a n i m p o r -tant role t o play in material properties, it h a s been impossible to quantify the effect. Except for very carefully controlled situations, all materials contain defects so that physical properties obtained from m e a s u r e m e n t s will include 91 92 Crystal Defects [Ch. 5 the effect of defects. If these are isolated vacancies, their presence will n o t be detectable even by electron microscopy. In the case of calculation, any poten-tial which is fitted to these experimental results will also reflect the effect of the defects which were present w h e n the m e a s u r e m e n t s were m a d e . P r o b a b l y the reason that the connection o n a fine a t o m i c level between material p r o p -erties a n d defect structure has n o t been possible is that the defect structure is, at present, not understood. In this chapter, the present state-of-the-art of defect structure will be reviewed a n d I expect that the connection with m a t e -rial properties will be m a d e in the near future. There are a n u m b e r of different types of defects which can be roughly classified as follows. T h e simplest defect is the point defect. This is a n atomic-size defect a n d can arise due to a n u m b e r of reasons. T h e first type, k n o w n as an interstitial, is d u e to an a t o m out of place a n d located between other a t o m sites. T h e second is k n o w n as a vacancy a n d is simply a vacant lattice site. T h e final general type is d u e t o a foreign a t o m located at a n otherwise vacant a t o m site. T h e case where two a t o m s of opposite sign are missing is k n o w n as a Schottky defect. W h e r e an a t o m exists as an interstitial a n d there is a corresponding vacancy, it is k n o w n as a Frenkel pair. Vacancies on adjoining sites are k n o w n as a divacancy. T h e study of the m o t i o n of vacan-cies is i m p o r t a n t in material processing. T h e vacancies can migrate to the surface as well as migrate away from interfaces. They m a y be either neutral or carry a charge. T h e latter case arises due to the breaking of b o n d s at a vacancy a n d the distortion of the electronic

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  Introduction to Crystal Growth

  Principles and Practice

  • H.L. Bhat(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Such a vacancy interstitial pair is called a Frenkel defect. Thus, a Frenkel defect ensures electrostatic neutrality. The presence of extra strain at the locations leads to an increase in the strain energy in the crystal and a disorder around them. However, the two positions need not be necessarily adjacent. If the number of Frenkel defects n is smaller than the number of lattice site N and the number of interstitial sites N ′ , the result is n NN e ( ) E k T 1/2 (– / 2 ) t ≈ ʹ (4.5) where E t is the energy necessary to move the atom from lattice site to an interstitial position. 1. Self interstitial atom 3 2 1 5 4 2. Vacancy 3. Frenkel 4. Substitutional impurity atom 5. Interstitial impurity atom FIGURE 4.1 Different types of point defects. 40 Introduction to Crystal Growth Interstitial Defect The converse of absence of an atom from a normally occupied site would be the presence of an atom in a normally unoccupied site, that is, a site in between normal lattice sites. Such an atom is called an interstitial. While we might expect a vacancy to cause a local increase of atomic separation, with the sur-roundings slightly in tension, the introduction of an interstitial will usually cause local squeezing and compression of the lattice. An interstitial may be self-interstitial wherein the same atom belonging to the lattice is misplaced in the interstitial position or it may be a foreign atom in the interstitial position. Interstitial impurity atoms are usually much smaller in size than the atoms of the bulk matrix. Both of these defects can be created by thermodynamic fluctuations or other effects resulting in the dislodging of an atom from its original site, which goes to either the surface or an interstitial site. Substitutional Defect Another type of point defect is an impurity atom, an atom of an abnormal type at a normal lattice site.

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  Materials Science and Engineering

  An Introduction

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

    (Publisher)

  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 94 • Chapter 4 / Imperfections in Solids defects. The necessity of the existence of vacancies is explained using principles of thermodynamics; in essence, the presence of vacancies increases the entropy (i.e., the randomness) of the crystal. The equilibrium number of vacancies N  for a given quantity of material (usually per meter cubed) depends on and increases with temperature according to N  = N exp ( − Q  kT ) (4.1) In this expression, N is the total number of atomic sites (most commonly per cubic meter), Q  is the energy required for the formation of a vacancy (J/mol or eV/atom), T is the absolute temperature in kelvins, 1 and k is the gas or Boltzmann’s constant. The value of k is 1.38 × 10 −23 J/atom∙ K, or 8.62 × 10 −5 eV/atom∙ K, depending on the units of Q  . 2 Thus, the number of vacancies increases exponentially with temperature—that is, as T in Equation 4.1 increases, so also does the term exp(−Q  /kT). For most metals, the fraction of vacancies N  /N just below the melting temperature is on the order of 10 −4 —that is, one lattice site out of 10,000 will be empty. As ensuing discussions indicate, a number of other material parameters have an exponential dependence on temperature similar to that in Equation 4.1. A self-interstitial is an atom from the crystal that is crowded into an interstitial site —a small void space that under ordinary circumstances is not occupied. This kind of defect is also represented in Figure 4.1. In metals, a self-interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated.

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  Introduction to the Physics and Chemistry of Materials

  • Robert J. Naumann(Author)
  • 2008(Publication Date)
  • CRC Press

    (Publisher)

  8 Defects in Crystals As we shall see, nature does not allow a crystal to be perfect, but even if it did, the performance of a perfect crystal would not necessarily be improved. In fact the defect structure very much determines the mechanical, electrical, thermal, optical, and magnetic properties of a material and our ability to understand the role of defects and to be able to control their formation is key to the development of useful materials. 8.1 What Are Defects? Generally speaking, defects are disruptions in the long-range order of the crystal that was discussed in Chapter 4. Such disruptions can range from an atom out of its place to gross defects such as voids or inclusions in the crystal. The mechanical properties of a material are largely in fl uenced by its defect structure and such defects are often engineered into the material to improve its properties. On the other hand, certain types of defects degrade the electronic and optical performance of materials used for these purposes and are to be avoided. Therefore, it is important to develop an understanding of how various types of defects arise in crystal and how to control them. The defects we will be concerned with can be classi fi ed into four categories: point defects, line defects, surface defects, and volume defects. The formation of these defects and their relation to the mechanical properties of the material are treated in the following sections. 8.2 Point Defects As the name implies, point defects involve atoms that are missing, out of place, impurities that were purposely added or those that crept in. 8.2.1 Vacancy Defects No crystal is perfect. No matter which solidi fi cation process is used or how careful one is in controlling the process, every crystal will have, at the very least, point defects known as vacancies. Vacancies arise spontaneously to minimize the free energy at the local temperature.

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  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)

  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. 4.7 Bulk or volume defects Other defects exist in all solid materials that are much larger than those heretofore discussed. These include pores, cracks, foreign inclusions, and other phases. They are normally introduced during processing and fabrication steps. Some of these defects and their effects on the properties of materials are discussed in subsequent chapters. 4.8 Atomic vibrations 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 defects. 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. With rising temperature, this average energy increases, and, in fact, the temperature of a solid is really just a measure of the average vibrational activity of atoms and molecules. At room temperature, a typical vibrational frequency is on the order of 10 13 vibrations per second, whereas the amplitude is a few thousandths of a nanometre. Many properties and processes in solids are manifestations of this vibrational atomic motion. For example, melting occurs when the vibrations are vigorous enough to rupture large numbers of atomic bonds. A more detailed discussion of atomic vibrations and their influence on the properties of materials is presented in a later chapter. MICROSCOPIC EXAMINATION 4.9 Basic concepts of microscopy FIGURE 4.13 Cross‐section of a cylindrical copper ingot.

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  Metals and Materials

  Science, Processes, Applications

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

    (Publisher)

  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. lack long-range order; we will therefore concentrate upon crystal defects. Defects in crystalline macro-molecular structures, as found in polymers, form a special subject and will be dealt with separately in Section 4.6.7. 4.2 Point defects 4.2.1 Point defects in metals Of the various lattice defects the vacancy is the only species that is ever present in appreciable concentra-tions in thermodynamic equilibrium and increases exponentially with rise in temperature, as shown in 88 Metals and Materials 700 r O 600 l· 0 ' ω 1 500 | ω Q. Φ 400 I 300 -J 6 x 10 Vacancy concentration Figure 4.2 Equilibrium concentration of vacancies as a function of temperature for aluminium (after Bradshaw and Pearson, 1957). Figure 4.2. The vacancy is formed by removing an atom from its lattice site and depositing it in a nearby atomic site where it can be easily accommodated. Favoured places are the free surface of the crystal, a grain boundary or the extra half-plane of an edge dislocation. Such sites are termed vacancy sources and the vacancy is created when sufficient energy is available (e.g. thermal activation) to remove the atom. If E { is the energy required to form one such defect (usually expressed in electron volts per atom), the total energy increase resulting from the forma-tion of n such defects is nE { . The accompanying entropy increase may be calculated using the relations S = k In W, where W is the number of ways of distributing n defects and N atoms onN + n lattice sites, i.e.

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  Physical Basis Of Plasticity In Solids

  • Jean-claude Toledano(Author)
  • 2011(Publication Date)
  • World Scientific

    (Publisher)

  Defects can be classified according to their “dimensionality”. Thus, one can consider point defects (zero-dimensional). For this type of defects, the volume of the perturbed region of a crystal is of the same order of 1 Other important physical properties of solids are also determined by the occurence of defects, such as, for instance, the electrical resistivity of metals. 51 52 Vacancies, an example of point defects in crystals magnitude as the volume of a single atom, or of a few atoms. A simple example is the vacancy consisting in the absence of an atom in a site nor-mally occupied by a constituent of the crystal (Fig. 4.1). Another simple example is the interstitial , i.e. an additional atom located in a normally empty space situated between the constituting-atoms of the structure (as the case of the carbon atoms in the iron structure described in chapter 2, section 4). A solid can also have substitutional impurities . These are atoms occupying a site of the crystal-structure normally occupied by an atom of different chemical nature. More complex point defects also exist, consisting of clusters (groups) of the preceding simple defects. (a) (b) (c) Figure 4.1 Three examples of point defects. (a) Vacancy. (b) Interstitial atom. (c) Substitutional atom. A linear defect (one-dimensional) is a filamentary (thread-shaped) de-fect, such as, for instance, the absence of a row of atoms in a crystal. The section of such a defect has the same order of magnitude as the section of an atom or of a few atoms, while its length is large as compared to the atomic dimensions, and can be as large as the linear size of the macroscopic crystal sample. This class of defects contains the dislocations, which, as mentioned in chapter 1, play a central role in the mechanism of plasticity. Their detailed description and properties will be analyzed in the next three chapters. In anticipation, Fig. 4.2 represents a simple type of dislocation, the so-called straight edge dislocation.

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  Materials Science for Engineers

  • J.C. Anderson, Keith D. Leaver, Rees D. Rawlings, Patrick S. Leevers(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  Thus D = D 0 exp(-E 0 /kT) (8.3) where the factor D 0 is normally a constant. This equation, introduced in the previous chapter, is almost universally applied to diffusion mechanisms in solids. 8.3.1 Substitutional impurity diffusion: a mechanism involving vacancies The value of the diffusion coefficient D of any atomic species depends on the detailed mechanism by which the diffusion occurs. If we were to imagine an ideal crystal in which there were no vacancies or defects, it would obviously be difficult for foreign atoms to penetrate the crystal, and they could only do so into interstitial positions. Thus diffusion of substitutional impurities normally differs significantly from the diffusion of interstitials. 164 CRYSTAL DEFECTS Fig. 8.5 The diffusion of an impurity atom through a crystal: (a) initial position with adjacent vacancy; (b) the activated step; (c) new position exchanged with vacancy; (d) potential energy variation of impurity atom during the diffusion process. There will always be a few vacancies in the lattice because of thermal agitation, where an atom has moved from its regular site in the lattice into an interstitial position (a Frenkel defect). If this interstitial atom diffuses away from the vacancy, the latter becomes a Schottky defect. Thus a substitutional impurity can diffuse most readily through the crystal if a neighbouring site is occupied by a vacancy. In diffusing, therefore, the impurity atom changes places with a neighbouring vacancy, effectively jumping from vacancy to vacancy as illustrated in Fig. 8.5. Whether it is able to move from one vacancy to the next will depend on the availability of a vacant neighbouring site, and the probability of this being available will be the probability of an adjacent atom jumping out of its lattice site to form a Frenkel defect. We therefore have two activated processes involved sequentially in the diffusion mechanism.

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  Imperfections in Crystalline Solids

  • Wei Cai, William D. Nix(Authors)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  However, the material introduced here will be needed in Sections 6.2 , 6.3 , and 7.4 . The chemical potential μ of the point defects has many similarities with the formation Gibbs free energy g f of the defects, e.g. they both have enthalpic and entropic contributions, but they are not identical. The chemical potential is more convenient to use than the formation Gibbs free energy in a number of scenarios. For example, the impurity atoms in the crystal may exist in the gas phase when taken out of the crystal, such as hydrogen in nickel. The equilibrium concentration of the impurity in the crystal depends on the pressure of the gas. This dependence can be derived most conveniently using the chemical potential, as will be shown below. Another example is the diffusion of point defects driven by non-equilibrium conditions. The variation of the chemical potential in space provides the driving force for diffusion, as will be shown in Section 7.4 . Point defects diffuse in a way that tends to reduce this variation. The equilib-rium condition is reached if and only if the chemical potential is constant everywhere in the crystal. 5.4.1 Interstitial point defects To properly define the chemical potential for interstitial point defects, we need to define a process in which the solute atom (B) is taken from some reference state and placed onto an unoccupied interstitial site inside the host crystal. The reference state is a hypothetical material for which the chemical potential for B atoms is defined to be zero. For simplicity, we consider the reference state as a perfect crystal formed entirely by B atoms, as shown in Fig. 5.13 . The reference crystal is always under zero stress, even though the host crystal for the Interstitial Defects can be subjected to non-zero stress. Let N s be the total number of interstitial sites in the crystal, N B be the actual number of Interstitial Defects, and χ i = N B / N s .

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