MATSCI 201 Lecture 7 Imperfections in Solids PDF Fall 2024

University of Science and Technology MATSCI 201 Fundamentals of Materials Science and Engineering LECTURE 7:Imperfections in Solids By: Dr. Worood A. El-Mehalmey, PhD. 13/11/2024 Materials Science Program...

University of Science and Technology MATSCI 201 Fundamentals of Materials Science and Engineering LECTURE 7:Imperfections in Solids By: Dr. Worood A. El-Mehalmey, PhD. 13/11/2024 Materials Science Program 1  MATSCI 201 Lecture 7: Imperfections in Solids q Introduction q Point Defects Vacancy Self-Interstitial q Impurities in Solids Solid Solution ü Substitutional ü Interstitial q Specification of Composition q Linear Defects Dislocations ü Edge ü Screw 2 Chapter 4: Imperfections in Solids Introduction: It has been tacitly assumed that perfect order exists throughout crystalline materials on an atomic scale. à However, such an idealized solid does not exist; all contain large numbers of various DEFECTS or IMPERFECTIONS. Why Study Imperfections in Solids? As a matter of fact, many of the properties of materials are profoundly sensitive to deviations from crystalline perfection à The influence is not always adverse à Often specific characteristics are deliberately fashioned by the introduction of controlled amounts or numbers of particular defects 3 Chapter 4: Imperfections in Solids Example: ü ATOMIC DEFECTS are responsible for reductions of gas pollutant emissions from today’s automobile engines. 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 crystalline metallic materials found in the catalytic converter. While attached to these sites, the molecules experience chemical reactions that convert them into other, non-polluting or less-polluting substances. Schematic diagram showing the location of the catalytic converter in an automobile’s exhaust system. 4 Chapter 4: Imperfections in Solids Introduction: A CRYSTALLINE DEFECT refers to a lattice irregularity having one or more of its dimensions on the order of an atomic diameter. Classification of crystalline imperfections is frequently made according to the geometry or dimensionality of the defect. 1) Point defects à those associated with one or two atomic positions à Vacancy, Interstitial or Substitutional atoms. 2) Linear defects à one-dimensional à dislocations. 3) Planar defects à two-dimensional à grain boundaries. 4) Bulk defects à pores and inclusions. 5 Chapter 4: Imperfections in Solids Point Defects: The simplest of the point defects is a VACANCY, or vacant lattice site, one normally occupied but from which an atom is missing. All crystalline solids contain vacancies, and, in fact, it is not possible to create such a material that is free of these 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. Vacancy vacant atomic sites in a structure Scanning probe micrograph that shows a vacancy on a (111)-type surface plane for silicon. 6  Chapter 4: Imperfections in Solids Point Defects: Vacancy The equilibrium number of vacancies (N!) for a given quantity of material (usually per meter cubed) depends on and increases with temperature according to: à The number of vacancies increases exponentially with temperature. "# "# Ln " " &' Exponential Increase Slope = ( % Activation Energy: The energy required $ $ for the formation of a vacancy (J/mol. or eV/atom) 7 Chapter 4: Imperfections in Solids Point Defects: Vacancy Calculate the equilibrium number of vacancies per cubic meter for copper at 1000°C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000°C) for copper are 63.5 g/mol. and 8.4 g/cm3, respectively. T= 1000°C à 1000 + 273 K Qv = 0.9 eV/atom "$ & ! "= Aw = 63.5 g/mol. '( ! = 8.4 g/cm3 à 8.4 * 106 g/m3 8 Chapter 4: Imperfections in Solids Point Defects: 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. à It introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated. The formation of this defect is not highly probable, and it exists in very small concentrations that are significantly lower than for vacancies. Self-Interstitial 9 Chapter 4: Imperfections in Solids Point Defects: A pure metal consisting of only one type of atom just isn't possible; IMPURITY OR FOREIGN ATOMS are always present, and some exist as crystalline point defects. In fact, even with relatively sophisticated techniques, it is difficult to refine metals to a purity in excess of 99.9999% à At this level, on the order of 1022 to 1023 impurity atoms are present in1 m3 of material. Most familiar metals are not highly pure; rather, they are ALLOYS, in which impurity atoms have been added intentionally to impart specific characteristics to the material à Ordinarily, alloying is used in metals to improve mechanical strength and corrosion resistance. For example à sterling silver is a 92.5% silver/ 7.5% copper alloy. Pure silver is highly corrosion resistant, but also very soft. Alloying with copper significantly 10 enhances the mechanical strength without depreciating the corrosion resistance appreciably. Chapter 4: Imperfections in Solids Point Defects: Impurities in solids The addition of impurity atoms to a metal results in the formation of: A. Solid Solution Depending on the kinds of impurity, their B. Or New Second Phase concentrations, and the temperature of the alloy. With regard to alloys, à Solvent is the element or compound that is present in the greatest amount; on occasion, solvent atoms are also called host atoms. à Solute is used to denote an element or compound present in a minor concentration. 11 Chapter 4: Imperfections in Solids Impurities in Solids: Solid Solution A solid solution forms when, as the solute atoms are added to the host material, the crystal structure is maintained and no new structures are formed. A solid solution is also compositionally homogeneous; the impurity atoms are randomly and uniformly dispersed within the solid. 12 Chapter 4: Imperfections in Solids Impurities in Solids: Solid Solution Impurity point defects are found in solid solutions, of which there are two types: ü Substitutional: solute or impurity atoms replace or substitute for the host atoms. ü Interstitial: impurity atoms fill the voids or interstices among the host atoms. 13 Chapter 4: Imperfections in Solids Solid Solution: Substitutional Several features of the solute and solvent atoms determine the degree to which the solute dissolves in the solvent. These are expressed as four Hume–Rothery Rules, as follows: 1. Atomic size factor. Appreciable quantities of a solute may be accommodated in this type of solid solution only when the difference in atomic radii between the two atom types is less than about ±15% à Otherwise, the solute atoms create substantial lattice distortions and a new phase forms. 2. Crystal structure. the crystal structures for metals of both atom types must be the same. 3. Electronegativity factor. The more electropositive one element and the more electronegative the other, the greater the likelihood that they will form an intermetallic compound instead of a substitutional solid solution. (Close) 4. Valences. a metal has more of a tendency to dissolve another metal of higher valency than to dissolve one of a lower valency. 14 Chapter 4: Imperfections in Solids Solid Solution: Substitutional An example of a substitutional solid solution is found for COPPER AND NICKEL. These two elements are completely soluble in one another at all proportions. ü The atomic radii for copper and nickel are 0.128 and 0.125 nm, respectively, ü Both have the FCC crystal structure. ü Their electro-negativities are 1.9 and 1.8. ü The most common valences are +1 for copper (although it sometimes can be +2) and +2 for nickel. 15 Chapter 4: Imperfections in Solids Solid Solution: Interstitial For both FCC and BCC crystal structures, there are two types of interstitial sites: ü Tetrahedral These are distinguished by the number of nearest ü Octahedral neighbor host atoms—that is, the coordination number. Octahedral à Coordination number = 6 Tetrahedral à Coordination number = 4 16 Chapter 4: Imperfections in Solids Solid Solution: Interstitial Compute the radius r of an impurity atom that just fits into a BCC octahedral site in terms of the atomic radius R of the host atom (without introducing lattice strains). BCC à a à 17 Chapter 4: Imperfections in Solids Specification of Composition: It is often necessary to express the composition (or concentration) of an alloy in terms of its constituent elements. à The Two Most Common ways to specify composition are; ü Weight (or mass) percent. ü Atom percent. The basis for weight percent (wt.%) à is the weight of a particular element relative to the total alloy weight. Weight Percent Atom Percent m1= mass of component 1 nm1= number of moles of component 1 18 Chapter 4: Imperfections in Solids Specification of Composition: Determine the composition, in atom percent, of an alloy that consists of 97 wt.% aluminum and 3 wt.% copper. (Aw of Cu= 63.55g/mol., and Aw of Al= 26.98g/mol.) 19 Chapter 4: Imperfections in Solids Linear Defects: A dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned. A dislocation produces permanent (plastic) deformation / slip systems. There are TWO TYPES of dislocations: ü Edge dislocations (Line dislocations). ü Screw dislocations. 20 Chapter 4: Imperfections in Solids Linear Defects: Edge Dislocation It is a linear defect that centers on the line that is defined along the end of the extra half-plane of atoms. It is represented by the symbol ⊥, which also indicates the position of the dislocation line. An edge dislocation may also be formed by an extra half-plane of atoms that is included in the bottom portion of the crystal; its designation is a ⊤. 21 Chapter 4: Imperfections in Solids Linear Defects: Screw Dislocation It is formed by a shear stress that is applied to produce the distortion. It is represented by the symbol ↻. 22 Chapter 4: Imperfections in Solids Microscopic Examination: Dislocations can be observed in crystalline materials using electron-microscopic techniques. A TEM of a titanium alloy in which the dark lines are 23 dislocations Summary: 24 25 26