Physics
Vacancy Defect
A vacancy defect refers to a type of crystal lattice imperfection where an atom is missing from its regular position in the lattice structure. This creates a vacant site within the crystal. Vacancy defects can affect the physical and chemical properties of materials, such as altering their electrical conductivity and thermal properties.
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12 Key excerpts on "Vacancy Defect"
- 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.
eBook - PDF- 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
eBook - PDFMetals 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.
eBook - PDF- Jean-claude Toledano(Author)
- 2011(Publication Date)
- World Scientific(Publisher)
Chapter 4 Vacancies, an example of point defects in crystals Main concepts: Dimensional classification of defects. Existence of stable defects at thermodynamic equilibrium. Formation and migration energies of point de-fects. Jump mechanism of vacancies. Random walk. Diffusion. 4.1 Classification of defects in crystals A crystal defect consists in any deviation from the strict periodicity of the ideal (infinite) crystal described in chapter 2. Its relevance in a book de-voted to the plastic behaviour of solids comes from the fact that it is the very existence of defects which explains the characteristics of this behaviour. 1 The occurence of a defect always increases the energy of a crystalline solid. Indeed, the ideal periodic structure is believed to correspond to the lowest energy of the assembly of atoms constituting the solid. Consequently, at very low (absolute zero) temperature, the stable state of the solid, which then corresponds to its lowest energy, will be defect-free. However, at any other temperature, the thermodynamic equilibrium of a system is not de-termined by its sole energy, as will be recalled in section 4.2, and a real solid will differ from the ideal crystal model. Certain types of defects will be its intrinsic constituants. By contrast, other types of defects (in par-ticular dislocations) should not be present at thermodynamic equilibrium. Their actual existence is due either to the out-of-equilibrium procedure of elaboration of the solid, or to the effect of specific external forces. 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
eBook - PDFIntroduction to Crystal Growth
Principles and Practice
- H.L. Bhat(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
37 4 Defects in Crystals An ideal crystal in which every lattice site is occupied by an atom, a molecule, or a group of atoms is a geometric concept. In real crystals, a vari-ety of deviations from the ideal lattice structure occur. Any deviation from the perfect atomic arrangement in a crystal is considered an imperfection or a defect. It has now become clear that many important properties of solids are controlled as much by imperfections as by the nature of the host crys-tal, which may act only as a solvent or matrix for the imperfections. As we know, the electrical conductivity of doped semiconductors is entirely due to a trace amount of intentionally added impurities. Considerable deviations from the theoretical values of the measured intensities of x-rays diffracted from crystals occur due to the presence of defects. The colors of many crys-tals are due to imperfections. Luminescence in crystals is nearly always con-nected to the presence of impurities. Diffusion of atoms through solids may be accelerated enormously by impurities and imperfections, and finally the mechanical properties of solids are usually controlled by imperfections. Imperfections or defects in the crystalline lattice are of different kinds. They are usually classified according to their geometrical nature as point, line, surface, and volume defects. As the names themselves indicate, a point defect has the center of disruption at a point in the structure, line imperfec-tion causes disruption along a line, surface defect is found along a surface, and volume defect is manifested in the bulk . Following are the commonly observed defects in crystals under each category (Table 4.1). In addition to these, one can also include excitons and polarons to the list under point defects. However, because of their special nature, these are not discussed here.
eBook - PDF- Richard J. Borg, G. J. Dienes(Authors)
- 2012(Publication Date)
- Academic Press(Publisher)
II Point Defects in Elemental Crystalline Substances All real crystals are imperfect containing both line and point defects and this chapter is devoted to their energetics because of their frequent and important role in solid state diffusion. The former, most commonly referred to as dislocations, have a minor influence on the chemistry of solids; although they are dominant in governing the strength properties and are frequently influential in the nucleation of phase transformations; we will consider their influence upon diffusion briefly in a later chapter. A point defect can be defined as any rational lattice point which is not occupied by the proper atom, ion, or molecule necessary to preserve the inherent periodicity of the structure, or the occupancy of a non-rational position by any of the foregoing. Generally, point defects are vacant lattice positions or interstitial atoms, but the term is sometimes enlarged to include trace amounts of impurities. It is, in a sense, the diffusion of point defects through the crystal structure which constitutes the making and breaking of chemical bonds; hence, they are primarily responsible for the occurrence of chemical reactions in solids. In addition, point defects are influential in determining the electrical behavior of extrinsic semiconductors, are respon-sible for color centers, control certain mechanical properties (e.g., second stage creep), and are the net result of radiation damage to solids. Because the laws and relationships governing the geometry, concentration, and mobility of point defects do not depend upon the exact chemical nature of 25 26 II Point Defects in Elemental Crystalline Substances the host crystal, it is convenient to treat the chemistry and physics of defects as separate entities.
eBook - PDF- R. E. Smallman(Author)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 9 Point defects in crystals 9.1 Introduction Of the various lattice defects which can exist in a metal, the vacancy is the only species that is ever present in appreciable concentrations in thermodynamic equilibrium. The equilibrium concentration increases exponentially with rise in temperature as shown in Figure 4.7 and, as a consequence, a knowledge of their behaviour is essential for understanding the deformation properties of metals particularly at elevated temperatures. The everyday industrial processes of annealing, homogenization, precipitation, sintering, surface hardening, as well as oxidation and creep, all involve, to varying degrees, the transport of atoms through the lattice with the help of vacancies. Similarly, vacancies enable dislocations to climb, since to move the extra half-plane of a dislocation up or down requires the mass transport of atoms. This mechanism is extremely important in the process of polygonization and recovery {see Chapter 10) and, moreover, such a mechanism enables dislocations to climb over obstacles lying in their shp plane, which illustrates one way in which metals can soften and lose their resistance to creep at high temperatures. The role of vacancies at high temperatures, where an appreciable concentra-tion is thermally maintained, is therefore well established. However, their importance in influencing the behaviour of metals at lower temperatures, i.e. around room temperature, is not so fully understood. It is for this reason that experiments on crystals made defective by quenching or irradiation now play a role in fundamental studies of metals far greater than their apparent ultimate importance. 9.2 The production of vacancies There are five main methods of introducing point defects into a metal in excess of the equilibrium concentration (we are here chiefly concerned with vacancies rather than interstitials): 1.
- Peter F. Green(Author)
- 2005(Publication Date)
- CRC Press(Publisher)
Structure, Defects and Atomic Diffusion in Crystalline Metals 101 where v v is the volume associated with a vacant site and v a is that of an atomic site; ∆ v v is the local reduction ( b < 1). If we imagine that there are N v vacant sites and N L lattice sites, then the average volume associated with a site in this crystal is 3.44 assuming the rule of mixtures. The difference between the volume per site of a perfect crystal and the crystal containing defects is, 3.45 This equation can be rewritten to yield 3.46 If we assume that the lattice parameter increases from a to a + ∆ a , then 3.47 The total volume of the crystal with vacancies is 3.48 If the volume of the perfect crystal, V = N L v a , is subtracted from V c , and assuming that the sample is a cube and that the length increases from l to ∆ l , then 3.49 A comparison of Eq. 3.42 and 3.44 leads to Eq. 3.42 for the vacancy concen-tration. Experiments confirm the exponential dependence of X v on temper-ature in metals. The foregoing example involved measurements of samples in which vacancies would be the primary defect. However, if a sample contained vacancies and self interstitials, then for a cubic crystal, 3.50 would imply that vacancies are the predominant defects, whereas would imply that self interstitials would be dominant. 〈 〉 = + − v N N v N N N v v L v L v L a 〈 〉 − = + − − = − v v N N v N N N v v X v X v a v L a L v L a a v a v a b b 〈 〉 − = = − v v v v v X a a v ∆ ( ) b 1 3 1 ∆ a a X v = − ( ) b V N v N v c v a L a = + b 3 ∆ l l X v = b X X l l a a v T i T − = − 3 ∆ ∆ 3 0 ( ) ∆ ∆ l l a a − > 3 0 ( ) ∆ ∆ l l a a − < 102 Kinetics, Transport, and Structure in Hard and Soft Materials It should be noted that self-interstitials are typically not the predominant defect under equilibrium conditions. The strain fields associated with self-interstitials typically extends beyond a single lattice position, which largely explains the large formation energies compared to vacancies.
eBook - PDF- R. E. Smallman, A.H.W. Ngan(Authors)
- 2011(Publication Date)
- Butterworth-Heinemann(Publisher)
(a) (b) (c) (d) Figure 3.1 (a) Vacancy–interstitial. (b) Dislocation. (c) Stacking fault. (d) Void. 95 96 Physical Metallurgy and Advanced Materials 700 600 500 400 300 0 1 2 3 4 5 6 10 4 Temperature ( C) Vacancy concentration Figure 3.2 Equilibrium concentration of vacancies as a function of temperature for aluminum (after Bradshaw and Pearson, 1957). In the following sections this type of classification will be used to consider the defects which can occur in metallic and ceramic crystals. 3.2 Point defects 3.2.1 Point defects in metals Of the various lattice defects the vacancy is the only species that is ever present in appreciable con-centrations in thermodynamic equilibrium and increases exponentially with rise in temperature, as shown in Figure 3.2. 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. Favored 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 activa-tion) to remove the atom. If E f is the energy required to form one such defect (usually expressed in electron volts per atom), the total energy increase resulting from the formation of n such defects is nE f . The accompanying entropy increase may be calculated using the relations S = k ln W , where W is the number of ways of distributing n defects and N atoms on N + n lattice sites, i.e. ( N + n )! / n ! N ! Then the free energy, G , or strictly F , of a crystal of n defects, relative to the free energy of the perfect crystal, is F = nE f − k T ln[( N + n ) ! / n ! N ! ], (3.1) which by the use of Stirling’s theorem 1 simplifies to F = nE f − k T [( N + n ) ln( N + n ) − n ln n − N ln N ] . (3.2) The equilibrium value of n is that for which d F / d n = 0, which defines the state of minimum free energy as shown in Figure 3.3.
eBook - PDF- 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.
eBook - PDF- Wei Cai, William D. Nix(Authors)
- 2016(Publication Date)
- Cambridge University Press(Publisher)
In this technique wires are first quenched from a high temperature to establish a vacancy supersaturation at a low temperature and then heated to various moderate temperatures to allow the excess vacancies to diffuse to and annihilate at sinks. The electrical resistivity is used to monitor the concentration of vacancies. The jump rate of an interstitial solute atom in a host crystal is similarly governed by a Boltz-mann relation involving the activation free energy of migration g m i , although the interstital atom may not follow a straight path when jumping between two equivalent sites. The jump of a substitutional solute atom, on the other hand, often requires the assistance of a neighboring vacancy. As a result, the jump rate of a substitutional solute atom is governed by a Boltzmann relation involving the sum of the activation free energy of migration and the free energy of vacancy formation. The evolution of the concentration field of a large number of point defects, each making random jumps to neighboring sites, can be described by the diffusion equation. In crystals with no internal stress nor chemical inhomogeneity (and ignoring any interaction between the point defects), the flux of point defects is proportional to the negative of the concentration gradient. The proportionality constant is the diffusion coefficient, which is directly related to the jump rate of the individual point defects. For crystals subjected to non-uniform internal stresses, it is necessary, instead, to write the point defect flux in terms of the gradient of the chemical potential. As a result, in the absence of vacancy sources and sinks, the local equilibrium vacancy concentration is enhanced at locations of positive pressure. This pressure effect is opposite to that in a solid containing vacancy sources and sinks and subjected to a uniform pressure.
eBook - PDF- 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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