Unit Cell Defects PDF

UNIT-1 (Part 1) UNIT CELL A unit cell is the smallest repeating unit of a crystal lattice in a material. It is a three-dimensional structure that contains one or more atoms or molecules arranged in a specific pattern that is repeated throughout the entire crystal lattice. The unit cell provides a ba...

UNIT-1 (Part 1) UNIT CELL A unit cell is the smallest repeating unit of a crystal lattice in a material. It is a three-dimensional structure that contains one or more atoms or molecules arranged in a specific pattern that is repeated throughout the entire crystal lattice. The unit cell provides a basic framework for understanding the crystal structure of a material, including its symmetry, atomic packing, and other important properties. In solid state physics and materials science, the unit cell is a fundamental concept that is used to describe the crystal structure of various materials. The unit cell parameters, such as the length and angle of its edges and the angles between them, provide a way to characterize the crystal structure and its properties. The unit cell is important because it allows scientists to describe the crystal structure of a material in a systematic way, which in turn can provide insights into its physical, mechanical, and electrical properties. Types of Unit Cell Numerous unit cells together make a crystal lattice. Constituent particles like atoms and molecules are also present. Each lattice point is occupied by one such particle. 1. Primitive Cubic Unit Cell 2. Body-centered Cubic Unit Cell 3. Face centered cubic unit cell EFFECTIVE NUMBER OF ATOMS- Effective number of atoms per unit cell N, is different from total number of atoms per unit cell. The atom at the corner of a cubical unit cell has only 1/8 of it inside the boundary of that unit cell. The remaining 7/8 of it lies in the surrounding unit cells of the crystal. Similarly the atom at the face in FCC is shared 1/2 by that atom and 1/2 by the neighbouring atom. In BCC, the atom at the centroid is wholly occupied by that unit cell in which it lies. Thus the effective number of atoms are 1, 2 and 4 in SC, BCC and FCC respectively. Figures 4.10 a-b-c explain these details. Effective number of atoms for different unit cells are summarized in Table 4.2. Defects in Solids The term “defect” or “imperfection” is generally used to describe any deviation from the perfect periodic array of atoms in the crystal. The properties of some materials are extremely influenced by the presence of imperfections such as mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength, condition in semiconductors, which are termed structure sensitive are greatly affected by the- relatively minor changes in crystal structure caused by defects or imperfections. There are some properties of materials such as stiffness, density and electrical conductivity which are termed structure-insensitive, are not affected by the presence of defects in crystals. It is important to have knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials. Crystal imperfections can be classified on the basis of their geometry as Point Imperfection- As the name suggests, they are imperfect point-like regions in the crystal. VACANCY- Vacancy refers to a vacant atomic site in a crystal. At these sites the atoms are missing. One or more atoms may remain absent from their respective locations. The missing of atoms is random and not according to any rule. SUBSTITUTIONAL IMPURITY This defect refers to a foreign atom that substitutes a parent atom at its site in the crystal. Atoms marked A in figure is the foreign atoms. The substituting foreign atoms are called solute and the substituted (or dislodged) parent atoms are known as the solvent. INTERSTITIAL IMPURITY When a small sized foreign atom occupies a void space in the parent crystal (or its unit cell), the defect is known as interstitial impurity. Atoms marked A in figure is the interstitial atoms. FRENKEL’S DEFECTS- An ion, displaced from a regular locations to an interstitial location, in an ionic solid is called Frenkel’s defects. The ions of the two different kinds are known as cations and anoins.Cations are the smaller ions while anions are the larger ones. Cations may easily get displaced into the void. SCHOTTKY’S DEFECT- When a pair of the one cations and one anions are absent from an ionic crystal, the defects is called Schottky’s defect. LINE IMPERFECTION- In materials science, an edge dislocation is a type of crystallographic defect that occurs when an extra half-plane of atoms is introduced into a crystal lattice. This extra half-plane is known as the dislocation line, and it creates a region of localized stress and strain around the line. An edge dislocation is characterized by a step-like feature in the crystal lattice, where the extra half- plane of atoms creates a discontinuity in the lattice structure. The atoms above and below the dislocation line are in different positions, which creates a strain field around the dislocation. This strain field can affect the mechanical, electrical, and thermal properties of the material. Edge dislocations can be created in a variety of ways, including plastic deformation, thermal cycling, and irradiation damage. They are a common type of dislocation in many metals and alloys, and they play an important role in determining the mechanical properties of these materials. For example, edge dislocations can increase the yield strength of a material by impeding the motion of dislocations and preventing further plastic deformation. The study of dislocations is an important part of materials science and engineering, as it helps researchers and engineers understand the behavior and properties of materials at the atomic scale. Edge dislocations, in particular, are important because they can significantly influence the properties and performance of many engineering materials. SCREW DISLOCATION In materials science, a screw dislocation is a type of crystallographic defect that occurs when two parts of a crystal lattice are sheared by a certain amount, causing the atoms in the crystal to be displaced. The dislocation line in a screw dislocation runs along a helical path, which gives the dislocation its name. Unlike an edge dislocation, which results from an extra half-plane of atoms being inserted into the crystal lattice, a screw dislocation occurs when one part of the crystal lattice is twisted relative to another part. This twisting motion results in a mismatch of atomic positions along the dislocation line, which creates a localized stress field around the dislocation. The strain field created by a screw dislocation is different from that of an edge dislocation, and it affects the mechanical properties of the material in different ways. Screw dislocations are typically associated with plastic deformation and are important in the study of the mechanical behavior of materials. They can affect the strength, ductility, and fracture behavior of materials, and they play a key role in many manufacturing processes. Screw dislocations are found in many materials, including metals, semiconductors, and ceramics. They are commonly formed during the growth of crystals, and they can also be introduced through mechanical deformation or thermal processing. The study of screw dislocations is an important part of materials science and engineering, as it helps researchers and engineers understand how materials respond to external forces and how they can be engineered to optimize their properties. MIXED DISLOCATION A mixed dislocation is a type of crystallographic defect that has both edge and screw character. Unlike an edge or screw dislocation, which only has one type of deformation mechanism, a mixed dislocation has both a component of shear deformation and a component of displacement perpendicular to the slip plane. Mixed dislocations can be thought of as a combination of edge and screw dislocations, and they are more complex than either type of dislocation alone. They can be found in a variety of materials, and their behavior can be difficult to predict. SURFACE IMPERFECTIONS Surface imperfections in solids are defects or irregularities that occur on the surface of a solid material. These imperfections can affect the physical, mechanical, and chemical properties of the material and can play an important role in determining its behavior and performance. There are two type of surface imperfections: a) Grain boundary defects b) Twining GRAIN BOUNDARY DEFECTS Grain boundaries are the regions where two adjacent crystals or grains meet in a material. Grain boundary defects are imperfections or irregularities in these regions that can affect the properties and performance of the material. There are several types of grain boundary defects, including: Grain boundary sliding: This occurs when one grain slides past another at the boundary. It can cause the material to deform and can lead to failure under stress. Grain boundary voids: These are empty spaces or cavities at the grain boundary that can weaken the material. Grain boundary defects can be introduced during material processing or through exposure to high temperatures, radiation, or other environmental factors. They can have a significant impact on the performance and reliability of materials in various applications. TWIN OR TWINNING This defect is also called twin boundary. As the name implies, twin boundaries occur in pairs. The arrangement of atoms is such that one side of twin boundary is a mirror replica of the other side. As shown in Fig. 6.16, side A is a mirror image of side B. The zone CDEF is known as twinned zone. DE and FC are twin boundaries. Twins can form during the process of recrystallization or during plastic deformation of materials. Occurrence of twins is common in brass and metallic sheets. Twins in crystalline solids can be visualized by an optical microscope. VOLUME IMPERFECTIONS Volume imperfections, also known as 3-dimensional imperfections are found inside the solids these may form due to one or more of the following reasons. 1. foreign-particle inclusions 2.regions of noncrystallinity 3. Pores 4. Dissimilar natured regions The dimensions of these are of the order of tens of Å. The inclusions, pores etc. may be randomly located at one or many positions in the volume of the material. DISLOCATION STRENGTHENING MECHANISM- When metals are deformed, some of the energy is stored inside as strain energy associated with dislocations. Dislocations cause atomic lattice distortion, which creates regions of compressive, tensile, and shear strains on neighboring atoms. For example, atoms near the dislocation line are squeezed together, causing compressive strain. On the other hand, atoms below the dislocation line experience tensile strain. Shear strains also occur around dislocations. These strains affect the neighboring atoms' behavior and can influence the mechanical properties of the metal. When metals are deformed, the distortion of the atomic lattice around a dislocation line creates strain fields that extend into the surrounding atoms. These strain fields decrease in magnitude as you move away from the dislocation. When dislocations are close to each other, they can interact and create forces on each other. Two dislocations of the same type and orientation will repel each other, while two dislocations of opposite types will attract each other and cancel out. These interactions play an important role in strengthening metals.