Materials Science-L5 PDF

Defects or Imperfections in Crystals The arrangement of the atoms or ions in engineered materials contains imperfections or defects. These defects often have an effect on the properties of material, such as the mechanical properties (strength, hardness and ductility). Crystalline imperfections...

Defects or Imperfections in Crystals The arrangement of the atoms or ions in engineered materials contains imperfections or defects. These defects often have an effect on the properties of material, such as the mechanical properties (strength, hardness and ductility). Crystalline imperfections can be classified on the basis of their geometry as follows: 1. Point imperfections 2. Line imperfections 3. Surface imperfections 4. Volume imperfections. Point Imperfections Point defects (Imperfections) are disruptions in perfect atomic or ionic arrangements in a crystal structure. These imperfections may be introduced by movement of the atoms or ions when they gain energy by heating, during processing of the material, or by the intentional or unintentional introduction of impurities. Different kinds of point imperfections are: Vacancies: A vacancy is produced when an atom or an ion is missing from its normal site in the crystal structure, as in Figure (a). When atoms or ions are missing (i.e., when vacancies are present), the overall randomness or entropy of the material increases, which increases the thermodynamic stability of a crystalline material. 27 All crystalline materials have vacancy defects. Vacancies are introduced into metals and alloys during solidification, at high temperatures, or due to radiation damage. At room temperature (298 K), the concentration of vacancies is small, but the concentration of vacancies increases exponentially as the temperature increases, as shown by the following equation: −𝑄𝑣 𝑛𝑣 = 𝑛 𝑒𝑥𝑝 ( ) 𝑅𝑇 where nv: is the number of vacancies per cm3; n: is the number of atoms per cm3; Qv: is the energy required to produce one mole of vacancies, in cal/mol or Joules/mol; cal Joules R : is the gas constant, 1.987 or 8.314 ; and mol.K mol.K T: is the temperature in Kelvin. Due to the large thermal energy near the melting temperature, there may be as many as one vacancy per 1000 atoms. Example: Calculate the concentration of vacancies in copper at room temperature (25°C). What temperature will be needed to heat treat copper such that the concentration of vacancies produced will be 1000 times more than the equilibrium concentration of vacancies at room temperature? Assume that 20,000 cal are required to produce a mole of vacancies in copper. (The lattice parameter of FCC copper is 0.36151 nm). 28 Solution: There are four atoms per unit cell; therefore, the number of copper atoms per cm3 is 29 Interstitial Defects: An interstitial defect is formed when an extra atom or ion is inserted into the crystal structure at unoccupied position, as in Figure (b). Substitutional Defects: A substitutional defect is introduced when one atom or ion is replaced by a different type of atom or ion as in Figure (c) and (d). Examples of substitutional defects include incorporation of dopants such as phosphorus (P) or boron (B) into Si. Whether atoms or ions added go into interstitial or substitutional sites depends upon the size of guest atoms or ions compared to the size of host ions. 30 Schottky Defect: The removal of a positively charged ion to create a vacancy must be counter–balanced by the removal of a negatively charged ion in order to maintain neutrality. As in the case of a sodium chloride crystal, the removal of a positive sodium ion is balanced by the removal of a negative chlorine ion in order to maintain neutrality (see Figure): Frenkel Defect: If an interstitial ion moves from a normal point to an interstitial point, then the defect is known as Frenkel defect. In Figure, an ion moves from normal position at A to interstitial position at B. 31 Line Imperfections or Dislocations Line defect is the slip plane within the crystal (i.e. atoms dislocated from their normal lattice sites). There are three types of dislocations: the screw dislocation, the edge dislocation, and the mixed dislocation. (i) Edge Dislocation Fig.(a) shows a perfect crystal, the top sketch depicting a three-dimensional view and the bottom one showing the atoms on the front face. If one of these vertical planes does not extend from the top to the bottom of the crystal but ends part way within the crystal, as in Fig. (b), a dislocation is present. In the perfect crystal, the atoms are in equilibrium positions and all the bond lengths are of the equilibrium value. In the imperfect crystal on the right, just above the edge of the incomplete plane, the atoms are squeezed together and are in a state of compression. The bond lengths have been compressed to smaller than the equilibrium value. 32 (ii) Screw dislocation Consider the hatched area AEFD on the plane ABCD in Fig. (a). Let the top part of the crystal over the hatched area be displaced by one interatomic distance to the left with respect to the bottom part, as shown in Fig. (b). Screw dislocations are symbolically represented by clockwise or anticlockwise rotation. These two cases are referred to as positive and negative screw dislocations. (iii) Mixed Dislocations As shown in Figure, mixed dislocations have both edge and screw components, with a transition region between them. 33 Surface Imperfections There are two main sources of dislocations in crystals: (1) mishandling during grain growth, i.e. during solidification process and (2) mechanical deformation during metal working processes as rolling, extrusions, drawing and spinning. In surface imperfections, each atom bonding at the surface no longer is disrupted. The exterior surface may also be very rough, may contain tiny notches, and may be much more reactive than the bulk of the material. The microstructure of many engineered ceramic and metallic materials consists of many grains. A grain is a crystalline portion of the material within which the arrangement of the atoms is nearly identical. However, the orientation of the atom arrangement, or crystal structure, is different for each adjoining grain. This means (the arrangement of atoms in each grain is identical but the grains are oriented differently. A grain boundary, the surface that separates the individual grains, is a narrow zone in which the atoms are not properly arranged. That is to say, the atoms are so close together at some locations in the grain boundary that they cause a region of compression, and in other areas they are so far apart that they cause a region of tension. Figure (a) and (b), a micrograph of a stainless steel sample, shows grains and grain boundaries. 34 One method of controlling the properties of a material is by controlling the grain size. By reducing the grain size, we increase the number of grains and, hence, increase the amount of grain boundary area. Any dislocation moves only a short distance before encountering a grain boundary and being stopped, and the strength of the metallic material is increased. The Hall-Petch equation relates the grain size to the yield strength (𝜎𝑦 ), 𝐾 𝜎𝑦 = 𝜎𝑜 + √𝑑 where d is the average diameter of the grains, and 𝜎𝑜 and K are constants for the metal. Example: The yield strength of mild steel with an average grain size of 0.05 mm is 138 MPa. The yield stress of the same steel with a grain size of 0.007 mm is 276 MPa. What will be the average grain size of the same steel with a yield stress of 207 MPa? Assume the Hall-Petch equation is valid and that changes in the observed yield stress are due to changes in grain size. Solution: 𝐾 𝜎𝑦 = 𝜎𝑜 + √𝑑 Thus, for a grain size of 0.05 mm, the yield stress is 𝐾 138 = 𝜎𝑜 + √0.05 For the grain size of 0.007 mm, the yield stress is 𝐾 276 = 𝜎𝑜 + √0.07 35 Solving these two equations K = 18.43 MPa-mm1/2, and 𝜎𝑜 = 55.5 MPa. Now we have the Hall-Petch equation as 18.43 207 = 55.5 + √𝑑 d= 0.0148 mm ( or d=14.8 µm) ------------------------------------------------------ Optical microscopy is one technique that is used to reveal microstructural features such as grain boundaries that require less than about 2000 magnification. The process of preparing a metallic sample and observing or recording its microstructure is called metallography. One way to specify grain size is by using the ASTM grain size number (ASTM is the American Society for Testing and Materials). The number of grains per square inch (N) is determined from a micrograph of the metal taken at magnification 100. The number of grains per square inch N is entered into Equation and the ASTM grain size number n is calculated: 𝑁 = 2𝑛−1 A large ASTM number indicates many grains, and correlates with high strengths for metals and alloys. 36 Example: Suppose we count 16 grains per square inch in a photomicrograph taken at magnification 250. What is the ASTM grain size number? Solution: If we count 16 grains per square inch at magnification 250, then at magnification 100 we must have: 250 2 𝑔𝑟𝑎𝑖𝑛𝑠 𝑁=( ) × 16 = 100 = 2𝑛−1 100 𝑖𝑛2 log(100) = (𝑛 − 1) log(2) 2 = (𝑛 − 1) 0.301 𝑛 = 7.64 ---------------------------------- Volume Imperfections Volume imperfections can be foreign-particle inclusions, large voids or pores, or noncrystalline regions which have the dimensions of at least a few tens of Å. 37