Imperfections in atomic arrangements

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1 MME131: Lecture 9 Imperfections in atomic arrangements Part 2: 1D 3D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Classifications and characteristics of 1D 3D defects 1D defect dislocations 2D defects free surface, grain boundary, twin boundary 3D defects porosity, cracks, inclusions References: 1. Callister. Materials Science and Engineering: An Introduction 2. Askeland. The Science and Engineering of Materials Lec 09, Page 1/15

2 Linear defects Line defects, a.k.a. dislocations, are one-dimensional imperfections in crystal structure where a row of atoms have a local structure that differs from the surrounding crystal. These type of defects are almost always present in a real crystals. In a typical material, about 5 out of every 100 million atoms ( %) belongs to a line defect. In a 10-cm 3 chunk of material (about the size of a six-sided die), there will be about 1017 atoms belonging to line defects! Line defects have a dramatic impact on yielding (i.e., mechanical deformation) of materials. Characteristics of line defects Intrinsic defect Not equilibrium defects Concentrations not given by Boltzmann factors Given enough time and thermal energy, atoms will rearrange to eliminate dislocations Caused by processing conditions (how the material is made) and by mechanical forces that act on the material Line defects are identified by Dislocation line indicates position and orientation of dislocation Burger s vector describes unit slip distance (magnitude and direction ) Lec 09, Page 2/15

3 Classification of dislocations Edge dislocation - A dislocation introduced into the crystal by adding an extra half plane of atoms Screw dislocation - A dislocation produced by skewing a crystal so that one atomic plane produces a spiral ramp about the dislocation. Mixed dislocation - A dislocation that contains partly edge components and partly screw components. Edge dislocations Can be viewed as an extra half-plane of atoms inserted into the structure, which terminates somewhere inside the crystal. The termination of this half-plane of atoms creates a defect line (dislocation line) in the lattice (line DC in figure ). The edge dislocation is designated by a perpendicular sign, either if the plane is above the dislocation line, or T if the plane is below the dislocation line. edge dislocation Deformation occurs in material along the slip plane by the movement of dislocations. slip plane Lec 09, Page 3/15

Edge dislocations can be quantified using a vector called the Burger s vector, b, which represents the relative atomic displacement in the lattice due to the dislocation To determine Burger s vector:

4 Edge dislocations can be quantified using a vector called the Burger s vector, b, which represents the relative atomic displacement in the lattice due to the dislocation To determine Burger s vector: make a circuit from atom to atom counting the same number of atomic distances in opposite directions. If the circuit encloses a dislocation it will not close. The vector that closes the loop is the Burgers vector b. Burger s vector For edge dislocation, the Burger s vector is perpendicular to the dislocation line Screw dislocations A dislocation produced by skewing a crystal so that one atomic plane produces a spiral ramp about the dislocation Formed due to the application of a shear stress dislocation line The perfect crystal (a) is cut and sheared one atom spacing, (b) and (c). The left region of the crystal is then shifted/twisted one atomic distance upward relative to the right side of the crystal. The line along which shearing occurs is a screw dislocation. Lec 09, Page 4/15

5 The Burger s vector for a screw dislocation is constructed in the same fashion as with the edge dislocation. For screw dislocation, the Burger s vector is parallel to the dislocation line representation of defect line (OC ), Burger s circuit and Burger s vector in a screw dislocation Mixed Dislocations When a line defect has both an edge and screw dislocation component, a mixed dislocation results. In this case, the Burger s vector is neither parallel nor perpendicular to the dislocation line, but can be resolved into edge and screw components. The exact structure of dislocations in real crystals is usually more complicated. Edge and screw dislocations are just extreme forms of the possible dislocation structures. Most dislocations have mixed edge/screw character. Lec 09, Page 5/15

6 Dislocations in ceramic materials An edge dislocation in MgO showing the slip direction and Burgers vector Lec 09, Page 6/15

transmission electron micrograph of nickel showing dislocations (dark lines and loops) The interatomic bonds are

compressive zone Lattice Strain Edge dislocations introduce compressive, tensile, and shear lattice strains.

Strain drops radially with distance from dislocation core tensile zone When an impurity atom is added to the structure,

7 transmission electron micrograph of nickel showing dislocations (dark lines and loops) The interatomic bonds are significantly distorted only in the immediate vicinity of the dislocation line. This area is called the dislocation core. compressive zone Lattice Strain Edge dislocations introduce compressive, tensile, and shear lattice strains. Screw dislocations introduce shear strain only. Dislocations have strain fields arising from distortions at their cores. Strain drops radially with distance from dislocation core tensile zone When an impurity atom is added to the structure, it positioned itself at the compressive/tensile compressive zone depending on the stress filed created by the impurity atom. Lec 09, Page 7/15

8 Slip the motion of dislocation Slip is the movement of large numbers of dislocations to produce plastic deformation. Slip allows deformation without breaking ductility Though individual bonds must be broken for dislocation to move, new bonds are formed throughout the slip process Analogy caterpillars, carpets, worms When a shear stress is applied to the dislocation the atoms are displaced, causing the dislocation to move one atomic distance in the slip direction. Continued movement of the dislocation eventually creates a step, and the crystal is deformed. Motion of caterpillar is analogous to the motion of a dislocation. Lec 09, Page 8/15

9 Surface defects Surface defects Imperfections that form a two-dimensional plane within the crystal. Classes of surface defects 1. External surface 2. Grain boundary 3. Twin boundary External Surfaces Surface atoms have unsatisfied atomic bonds, and higher surface energies, g (J/m 2 or, erg/cm 2 ) than the bulk atoms. To reduce surface free energy, material tends to minimize its surface areas against the surface tension (e.g. liquid drop). Lec 09, Page 9/15

Grain Boundaries Polycrystalline material comprised of many small crystals or grains having different crystallographic orientations.

Segregation of impurities occurs at grain boundary. Dislocations can usually not cross the grain boundary.

(b) Grains and grain boundaries in a stainless steel sample.

10 Grain Boundaries Polycrystalline material comprised of many small crystals or grains having different crystallographic orientations. Atomic mismatch occurs within the regions where grains meet. These regions are called grain boundaries. Segregation of impurities occurs at grain boundary. Dislocations can usually not cross the grain boundary. (a) The atoms near the boundaries of the three grains do not have an equilibrium spacing or arrangement. (b) Grains and grain boundaries in a stainless steel sample. angle of misalignment Depending on misalignments of atomic planes between adjacent grains we can distinguish between the low and high angle grain boundaries high-angle grain boundary low-angle grain boundary angle of misalignment High angle grain boundaries cause greater mismatch along the grain boundary and offer greater resistance to dislocation motion Lec 09, Page 10/15

Hall-Petch equation The relationship between yield strength (s y ) and grain size (d) in a metallic material s y = s 0 + K d -1/2 Finer the grains, better are the mechanical properties The effect of

11 Hall-Petch equation The relationship between yield strength (s y ) and grain size (d) in a metallic material s y = s 0 + K d -1/2 Finer the grains, better are the mechanical properties The effect of grain size on the yield strength of steel at room temperature. The yield strength of mild steel with an average grain size of 0.05 mm is 20,000 psi. The yield stress of the same steel with a grain size of mm is 40,000 psi. Assuming that the Hall-Petch equation is valid, what will be the average grain size of the same steel with a yield stress of 30,000 psi? SOLUTION Example: Design of a mild steel For a grain size of 0.05 mm the yield stress is MPa = MPa. (Note: 1,000 psi = MPa). Using the Hall-Petch equation Lec 09, Page 11/15

For the grain size of 0.007 mm, the yield stress is 40 6.895 MPa = 275.8 MPa. Therefore, again using the Hall-Petch equation: Solving these two equations, we get K = 18.43 MPa-mm 1/2 σ 0 = 55.5 MPa. Now we have the Hall-Petch equation as σ y = 55.

12 For the grain size of mm, the yield stress is MPa = MPa. Therefore, again using the Hall-Petch equation: Solving these two equations, we get K = MPa-mm 1/2 σ 0 = 55.5 MPa. Now we have the Hall-Petch equation as σ y = d -1/2 If we want a yield stress of 30,000 psi or = MPa, the grain size will be mm. Grain Size Measurement ASTM grain size number (G) - A measure of the size of the grains in a crystalline material obtained by counting the number of grains per square inch using a magnification 100. N = 2 G-1 N = number of observed grains per square inch in area on photomicrograph taken at x100. G = ASTM grain size number Lec 09, Page 12/15

13 Example: Calculation of ASTM grain size number 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: N = (250/100) 2 (16) = 100 grains/in 2 = 2 G-1 ln 100 = (G 1) ln = (G 1)(0.693) G = 7.64 Twin Boundaries Special grain boundaries with mirrored atomic positions across the boundary. Produced by shear deformation of BCC/HCP materials (mechanical twin), or during annealing following deformation (annealing twin) of FCC materials. Application of a stress to the perfect crystal (a) may cause a displacement of the atoms, (b) causing the formation of a twin. Note that the crystal has deformed as a result of twinning. Lec 09, Page 13/15

A micrograph of twins within a grain of brass (x250) Twining gives rise to shape memory metals, which can recover their original shape if heated to a high temperature.

14 A micrograph of twins within a grain of brass (x250) Twining gives rise to shape memory metals, which can recover their original shape if heated to a high temperature. Shape-memory alloys are twinned and when deformed they untwin. At high temperature the alloy returns back to the original twin configuration and restore the original shape. Bulk or volume defects Pores affect optical, thermal, and mechanical properties Cracks affect mechanical properties Foreign inclusions affect electrical, mechanical, optical properties Lec 09, Page 14/15

15 Next Class MME131: Lecture 10 Diffusion in solids Lec 09, Page 15/15

Imperfections in the Atomic and Ionic Arrangements

Imperfections in the Atomic and Ionic Arrangements Objectives Introduce the three basic types of imperfections: point defects, line defects (or dislocations), and surface defects. Explore the nature and effects of different types of defects. Outline Point