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Crystal Imperfections-- Point, Line and Planar Defect

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Crystal Imperfections-- Point, Line and Planar Defect CRYSTAL IMPERFECTIONS: Introduction After studying the basics of crystallography, we arrived on one of the most important topics named Crystal Imperfection. Here we will be discussing the dimensional imperfection we encounter and its subtopics like the need to study, the cause behind the imperfection and the types of Imperfection we come across in a solid. We know about a crystal and its characteristics. And we also know that behind the ideality of theories in science, there is a reality of application in the true world. And in this topic, we will be encountering the reality. So, I will be defining an ideal crystal on the basis of facts provided to us till now. IDEAL CRYSTAL = Lattice + Motif An atom or group of 3 -D periodic atoms associated with each lattice arrangement of points Fig. 3-d representation of crystal of common salt The deviations we encounter in this set of ideal crystal, are termed as Defects or Imperfections. DEFINITION- Deviations in the regular geometrical arrangement of the atoms in a crystalline solid. Causes There can be a number of wanted and unwanted causes behind the defects that appear in a solid. Some are mentioned below: 1 .Deformation of solids (Alteration in size or shape of a body under the influence of mechanical forces) 2 3 4 .Rapid cooling from high temperature. .Crystallisation occurring at a differed rate. .High-energy radiation striking the solid. These reasons influence the mechanical, electrical, and optical behaviour of a crystal or a solid. Healthy Imperfections When we come across the word “Imperfection”, we assume that the thing for which this adjective is used is not perfect or worse than the perfect one. But this is not always true, sometimes we ourselves need this imperfection or defect to be inculcated in the solid, and often specific characteristics are deliberately fashioned by the introduction of controlled amount or numbers of particular defects. A catalytic converter is the pollutant-reducing device that is located in the automobile’s exhaust system. Molecules of pollutant gases become attached to surface defects of crystal-line metallic materials found in the catalytic converter. While attached to these sites, the molecules experience chemical reactions that convert them into other non or less polluting substances. Some more examples are as follows- 1 .For the processing of silicon as a semiconducting material, it is important to specify impurity concentration in appropriate units. 2 .The mechanism of hardening and strengthening for stell alloys involve a crystalline defect called dislocation. Why to Study The properties of some materials are profoundly influenced by the presence of imperfection. Consequently, it is important to have knowledge about the types of imperfections to have a knowledge about the types of imperfections that exist and the roles they play in affecting the behaviour of materials. For example- the mechanical properties of pure metals experience significant alteration when alloyed. For example, brass (70% copper and 30%zinc) is much harder and stronger than pure copper. Classification Based on dimensionality, we can classify the crystal defects broadly into three major types. 1 2 3 . Zero dimensional (Point defect: Vacancy or interstitial) . One dimensional (Line defect: Dislocation) . Two dimensional (Surface Defect) Point Imperfection Point imperfections are also referred to as zero-dimensional imperfections. As the name implies, they are imperfect point-like regions in the crystal. One or two atomic diameters is the typical size of a point imperfection. Different kinds of point imperfections are now described. There are 3 types of point defects: 1. Stoichiometric Defect 2. Non-stoichiometric Defect 3. Impurity Defect Stoichiometric Defect In this kind of point defect, the ratio of positive and negative ions (Stoichiometric) and electrical neutrality of a solid is not disturbed. Sometimes it is also known as intrinsic or thermodynamic defects. Fundamentally, in a non-ionic compound they are of three types: 1 . Vacancy Defect A vacancy refers to an atomic site from where the atom is missing, as shown in Fig. 6.1a. When an atom is not present at their lattice sites, then that lattice site is vacant and it creates a vacancy defect. Figure 6.1d depicts a vacancy in platinum photographed in a field ion microscope. 2 . Substitutional Impurity Defect A substitutional impurity (or solute) is a point imperfection. It refers to a foreign atom that substitutes for or replaces a parent atom in the crystal, see Fig. 6.1b. Aluminium and phosphorus doped in silicon are substitutional impurities in the crystal. 3 . Interstitial Impurity Defect An interstitial impurity is also a point imperfection. It is a small sized atom occupying the void space in the parent crystal, without dislodging any of the parent atoms from their sites, as shown in Fig. 6.1c. An atom can enter the interstitial void space only when it is substantially smaller than the parent atom. In close packed structures, the largest atom that can fit the octahedral and the tetrahedral voids have radii 0.414r and 0.225r, respectively, where r is the radius of the parent atom. For example, carbon is an interstitial solute in iron. It occupies the octahedral voids in the high temperature FCC form of iron. The iron atom in the FCC crystal has a radius of 1.29 Å, whereas the carbon atom has a radius of 0.71 Å (covalent radius in graphite). The carbon radius is clearly larger than 0.414 *1.29 = 0.53 Å, which is the size of the octahedral void. Therefore, there are strains around the carbon atom in the FCC iron, and the solubility is limited to 2 wt.%. In the room temperature BCC form of iron, the voids are still smaller and hence the solubility of carbon is very limited, that is, only 0.008 wt.%. An ionic compound shows mainly shows: Frenkel Defect In ionic crystals, the formation of point imperfections is subject to the requirement that the overall electrical neutrality is maintained. An ion displaced from a regular site to an interstitial site is called a Frenkel imperfection, see Fig. 6.2a. As cations are generally the smaller ions, it is possible for them to get displaced into the void space. Anions do not get displaced like this, as the void space is just too small for their size. A Frenkel imperfection does not change the overall electrical neutrality of the crystal. The point imperfections in silver halides and CaF2 are of the Frenkel type. Schottky Defect A pair of one cation and one anion can be missing from an ionic crystal as shown in Fig. 6.2b. The valency of the missing pair of ions should be equal to maintain electrical neutrality. Such a pair of vacant ion sites is called a Schottky imperfection. This type is dominant in alkali halides. Impurity Defects We know that trivalent cations such as Fe3+ and Cr3+ can substitute for trivalent parent Al3+ cations in the Al2O3 crystal. If, however, the valency of the substitutional impurity is not equal to the parent cation, additional point defects may be created due to such substitution. For example, a divalent cation such as Cd2+ substituting for a univalent parent ion such as Na+ will, at the same time, create a vacant cation site in the crystal so that electrical neutrality is maintained it creates an impurity defect. Non-stoichiometric Defects Defect structures are produced when the composition of an ionic crystal does not correspond to the exact stoichiometric formula. Such defect structures have an appreciable concentration of point imperfections. They are of two types: 1 . Metal deficiency defect The solids have less number of metals relative to described stoichiometric proportion.we can better understand by taking example of ZnO. In ZnyO, where y > 1, the excess cations occupy interstitial voids. Such a compound can be produced by heating a stoichiometric compound in zinc vapour. The two electrons released from each zinc atom that enters the crystal stays around an interstitial cation, as shown in Fig. 6.3a. 2 . Metal excess defect Here, solids have more number of metals relative to described stoichiometric proportion. Consider deviations from the stoichiometric formula in compound FeO. In FexO, where x < 1, vacant cation sites are present. Such a compound can be produced by heating a stoichiometric FeO in an oxygen atmosphere. The two electrons required by each excess oxygen atom is donated by two Fe2+ ions which become Fe3+ (ferric) ions, see Fig. 6.3b. Enthalpy of Formation of the Point Imperfections The presence of a point imperfection introduces distortions in the crystal. If the imperfection is a vacancy, the bonds that the missing atom would have formed with its neighbours are not there. In the case of an impurity atom, as a result of the size difference, elastic strains are created in the region of the crystal immediately surrounding the impurity atom. The elastic strains are present irrespective of whether the impurity atom is larger or smaller than the parent atom. A larger atom introduces compressive stresses and corresponding strains around it, while a smaller atom creates a tensile stress- strain field. Similarly, an interstitial atom produces strains around the void it is occupying. All these factors tend to increase the enthalpy (or the potential energy) of the crystal. The work required to be done for creating a point imperfection is called the enthalpy of formation (Hf ) of the point imperfection. It is expressed in kJ mol–l or eV/point imperfection. The enthalpy of formation of vacancies in a few crystals is shown in Table 6.1. By virtue of the fact that a point imperfection is distinguishable from the parent atom, the configurational entropy of a crystal increases from zero for a perfect crystal to positive values with increasing concentration of the point imperfection.
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