Physical Metallurgy

Step 1: Understanding dislocations.
Dislocations are line defects in crystals that play a crucial role in plastic deformation. Their generation and multiplication directly influence material strength.
Step 2: Frank-Read source mechanism.
The Frank-Read source is a well-known mechanism for the multiplication of dislocations. It involves a pinned dislocation segment that bows out under applied stress and produces new dislocation loops repeatedly.
Step 3: Eliminating other options.
(A) Schottky mechanism: Related to point defects such as vacancies, not dislocations.
(B) Burger’s vector: Describes the magnitude and direction of a dislocation but does not generate it.
(C) Twist: Refers to a type of grain boundary, not a dislocation generation process.
Step 4: Conclusion.
Thus, dislocations are generated by the Frank-Read source mechanism.

Step 1: Classification of crystal defects.
Crystal defects are categorized based on their dimensionality: zero-dimensional (point defects), one-dimensional (line defects), two-dimensional (surface defects), and three-dimensional (volume defects).
Step 2: Understanding grain boundaries.
Grain boundaries are interfaces between two crystals of different orientations. Since they extend over an area, they are considered two-dimensional defects.
Step 3: Analysis of other options.
(B) Point defect: Zero-dimensional defects such as vacancies.
(C) Line defect: One-dimensional defects like dislocations.
(D) Volume defect: Three-dimensional defects such as voids and inclusions.
Step 4: Conclusion.
Therefore, grain boundary defect is a two-dimensional defect.

Step 1: Understanding cast iron composition.
Cast iron contains more than 2% carbon, typically around 4.3% carbon, which corresponds to the eutectic composition in the iron–carbon phase diagram.
Step 2: Eutectic reaction in cast iron.
At 4.3% carbon, liquid iron transforms directly into a mixture of austenite and cementite at a constant temperature, which is known as a eutectic reaction.
Step 3: Analysis of other options.
(B) Isomorphous alloy: These alloys show complete solubility, which is not the case for iron–carbon systems.
(C) Peritectic alloy: Involves a different type of phase transformation.
(D) Peritectoid alloy: Occurs in solid-state reactions only.
Step 4: Conclusion.
Cast iron is correctly classified as a eutectic alloy.

Step 1: Understanding solidification in alloys.
Solidification of an alloy begins when the first solid phase starts to form from the liquid during cooling. In a phase diagram, this transformation is represented by a specific boundary line.
Step 2: Role of the liquidus line.
The liquidus line separates the fully liquid region from the liquid + solid region. As soon as the temperature crosses this line during cooling, solidification begins.
Step 3: Elimination of other options.
(B) Solidus line: Represents the completion of solidification, not the beginning.
(C) At equilibrium: Equilibrium is a condition, not a boundary for phase change.
(D) At freezing point: Pure metals freeze at a point, but alloys solidify over a range of temperatures.
Step 4: Conclusion.
Hence, the solidification of an alloy starts from the liquidus line.

Step 1: Understanding invariant reactions.
Invariant reactions involve transformation of phases at a fixed temperature and composition in phase diagrams. These reactions may occur in liquid–solid or solid–solid systems.
Step 2: Identifying the given reaction.
The reaction given is: This indicates a solid–solid reaction during cooling.
Step 3: Differentiating between reactions.
Eutectic: Liquid Solid 1 + Solid 2
Peritectic: Liquid + Solid Solid
Eutectoid: Solid Solid 1 + Solid 2
Peritectoid: Solid 1 + Solid 2 Solid 3
Step 4: Conclusion.
Thus, the given reaction represents a peritectoid reaction.

Step 1: Understanding coordination number.
The coordination number is the number of nearest neighboring atoms surrounding a given atom in a crystal structure.
Step 2: Structure of BCC crystal.
In a Body-Centered Cubic (BCC) structure, each atom at the center of the cube is surrounded by atoms located at the eight corners of the cube.
Step 3: Counting nearest neighbors.
Each atom in a BCC lattice has eight nearest neighboring atoms at equal distances.
Step 4: Conclusion.
Therefore, the coordination number of a BCC crystal is 8.

Step 1: Understanding nucleation.
Nucleation is the initial process during a phase transformation where small clusters of atoms form in the parent phase. These clusters may grow or dissolve depending on their size.
Step 2: Concept of critical radius.
There exists a critical radius ( ) during nucleation. Clusters with radius smaller than are unstable and tend to dissolve back into the parent phase.
Step 3: Definition of embryos.
Clusters or particles with radius less than the critical radius are called embryos. Only those clusters that grow beyond the critical radius become stable nuclei.
Step 4: Conclusion.
Hence, product particles having radius less than the critical radius are known as embryos.