Week 6 Lec 3 Ch 4.ppt PDF

CH 4 IMPERFECTIONS IN SOLIDS Chapter 3 -  Imperfections in Solids There is no such thing as a perfect crystal. What are these imperfections? Why are they important? Many of the important properties of materials are due to the presence of imperfections....

CH 4 IMPERFECTIONS IN SOLIDS Chapter 3 -  Imperfections in Solids There is no such thing as a perfect crystal. What are these imperfections? Why are they important? Many of the important properties of materials are due to the presence of imperfections. Chapter 3 - 2  Types of Imperfections Vacancy atoms Interstitial atoms Point defects Substitutional atoms Dislocations Line defects Grain Boundaries Area defects Chapter 3 - 3  Point Defects in Metals Vacancies: -vacant atomic sites in a structure. The simplest of the point defects is a vacancy, or vacant lattice site, one normally occupied from which an atom is missing. Vacancy distortion of planes Chapter 3 - 4  All crystalline solids contain vacancies and, in fact, it is not possible to create such a material that is free of these defects. Chapter 3 - 5  The equilibrium number of vacancies for a given quantity of material depends on and increases with temperature according to; In this expression, N is the total number of atomic sites, is the energy required for the formation of a vacancy, T is the absolute temperature1 in kelvins, and k is the gas or Boltzmann’s constant. Thus, the number of vacancies increases exponentially with temperature; that is, as T in Equation 4.1 increases, so also does the expression exp (-Qv/kT) Chapter 3 - 6  Equilibrium Concentration: Point Defects Equilibrium concentration varies with temperature! Activation energy, energy required No. of defects for the formation of a vacancy Nv  Q v  Total No. of potential  exp   N  kT  Temperature (K) defect sites or atomic sites Boltzmann's constant -23 (1.38 x 10 J/atom-K) -5 (8.62 x 10 eV/atom-K) Each lattice site is a potential vacancy site Chapter 3 - 7 Chapter 3 - 8 Chapter 3 - 9  Self-Interstitials: 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. The formation of this defect is not highly probable, and it exists in very small concentrations, which are significantly lower than for vacancies. -"extra" atoms positioned between atomic sites. self- interstitial distortion of planes Chapter 3 - 10  IMPURITIES IN SOLIDS A pure metal consisting of only one type of atom just isn’t possible; impurity or foreign atoms will always be present, and some will 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%. 22 23 At this level, on the order of 10 to 10 to impurity atoms will be present in one cubic meter of material. Chapter 3 - 11  IMPURITIES IN SOLIDS ALLOY 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. Ordinarily, alloying is used in metals to improve mechanical strength and corrosion resistance. For example, sterling silver is a 92.5% silver – 7.5% copper alloy. In normal ambient environments, pure silver is highly corrosion resistant, but also very soft. Alloying with copper significantly enhances the mechanical strength without depreciating the corrosion resistance appreciably. Chapter 3 - 12 Chapter 3 - 13  Solid Solutions 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. It is useful to draw an analogy with a liquid solution. If two liquids, soluble in each other (such as water and alcohol) are combined, a liquid solution is produced as the molecules intermix, and its composition is homogeneous throughout. A solid solution is also compositionally homogeneous; the impurity atoms are randomly and uniformly dispersed within the solid. Chapter 3 - 14 Impurity point defects are found in solid solutions, of which there are two types: substitutional and interstitial. For the substitutional type, solute or impurity atoms replace or substitute for the host atoms Chapter 3 - 15  Imperfections in Metals (i) Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random dist. of point defects) OR Substitutional solid soln. Interstitial solid soln. (e.g., Cu in Ni) (e.g., C in Fe) Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) Second phase particle -- different composition -- often different structure. Chapter 3 - 16  Imperfections in Metals (ii) Conditions for substitutional solid solution (S.S.) W. Hume – Rothery rule – 1. r (atomic radius) < 15% – 2. Proximity in periodic table i.e., similar electronegativities – 3. Same crystal structure for pure metals – 4. Valency All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency Chapter 3 - 17  Imperfections in Metals (iii) Application of Hume–Rothery rules – Solid Solutions Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity 1. Check Cu and Ni Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 Table on p. 118, Callister & Rethwisch 8e. Chapter 3 - 18  Composition It is often necessary to express the composition (or concentration) of an alloy in terms of its constituent elements. The two most common ways to specify composition are weight (or mass) percent and atom percent. The basis for weight percent (wt%) is the weight of a particular element relative to the total alloy weight. For an alloy that contains two hypothetical atoms denoted by 1 and 2, the concentration of 1 in wt%, is defined as Chapter 3 - 19  Impurities in Solids Specification of composition m1 – weight percent C1  x 100 m1  m2 m1 = mass of component 1 ' n m1 – atom percent C  1 x 100 n m1  n m 2 nm1 = number of moles of component 1 Chapter 3 - 20 Chapter 3 - 21 Chapter 3 - 22 Simultaneous Substitutional and Interstitial Alloying It's possible to have both substitutional and interstitial guest atoms coexisting in an alloy. This occurs when: Some guest atoms have a size similar to the host atoms and replace them at lattice sites (substitutional). Other guest atoms are much smaller and fit into the interstitial spaces (interstitial). Examples of Alloys with Both Substitutional and Interstitial Guests: 1.Steel (Fe-C-X alloy): 1. Substitutional guest atoms: Elements like Cr, Ni, Mo, or Mn can substitute for Fe atoms in the iron lattice. 2. Interstitial guest atoms: Carbon (C) occupies the interstitial spaces in the Fe lattice. 2.Titanium Alloys (Ti-Al-O): 1. Substitutional guest atoms: Aluminum (Al) substitutes for titanium (Ti) in the lattice. 2. Interstitial guest atoms: Oxygen (O), being smaller, occupies the interstitial spaces in the Ti lattice. Chapter 3 - 23 Applications: Advanced High-Strength Steels (AHSS): In these steels, elements like manganese (Mn), silicon (Si), and chromium (Cr) act as substitutional solutes, while carbon (C) remains in the interstitial positions. This results in a strong, ductile alloy. Superalloys: Alloys used in jet engines often feature substitutional alloying (e.g., with elements like Ni, Co, and Cr) combined with interstitial alloying (e.g., with carbon, nitrogen, or boron) to enhance mechanical properties at high temperatures. Chapter 3 - 24