ANS:B - square root of time

During decarburizing of a plain carbon steel, the thickness of the ferrite layer growth is typically proportional to the square root of time. Explanation:

1. Decarburization Process: Decarburization is a process where the surface of a steel material loses carbon due to exposure to high temperatures in an oxidizing atmosphere. This process commonly occurs during heat treatment processes such as annealing, carburizing, or when steel is heated in air.
2. Formation of Ferrite Layer: As carbon diffuses out of the steel surface, it leaves behind a layer of ferrite, which is a phase of iron with low carbon content. This ferrite layer forms gradually as carbon atoms diffuse away from the steel surface.
3. Rate of Ferrite Layer Growth: The rate at which the ferrite layer grows during decarburization is influenced by various factors, including temperature, carbon content of the steel, and time. However, experimental observations have shown that the thickness of the ferrite layer grows approximately proportional to the square root of the time of exposure.
4. Mathematical Relationship: Mathematically, if d represents the thickness of the ferrite layer and t represents the time of exposure, the relationship can be expressed as d∝t​.
5. Reasoning: The diffusion of carbon atoms through the steel matrix follows a diffusive process, where the rate of diffusion is inversely proportional to the square root of time according to Fick's laws of diffusion. This diffusion-controlled process governs the growth of the ferrite layer during decarburization, leading to a proportional relationship between the thickness of the ferrite layer and the square root of time.