Jawaharlal Nehru Technological University Hyderabad B.Tech III Fundamentals of Engineering Materials Previous Question Paper (September - 2021 - R16)

Grain size is a critical microstructural parameter that influences the mechanical properties of materials. The primary methods for determining grain size include:

1. Comparison Method (ASTM E112): This involves comparing the grain structure observed under a microscope with a set of standard ASTM grain size charts at a magnification of 100x. The grain size number (G) is determined by matching the grain density.
2. Planimetric Method: A known area is drawn on the micrograph, and the number of grains within that area is counted. Grains fully inside the area are counted as 1, and those intersecting the boundary are counted as 0.5. The grain density is then calculated to determine the average grain size.
3. Intercept Method: A line of known length is drawn across the micrograph. The number of grain boundaries intersected by the line is counted. The average grain diameter is calculated by dividing the total length of the line by the number of intersections, adjusted for magnification.

Miller indices (hkl) define the orientation of crystallographic planes. To draw these planes in a unit cell:

1. (201) Plane: Take the reciprocals of the indices (1/2, 1/0, 1/1), which gives intercepts at 0.5 on the x-axis, infinity on the y-axis (parallel to y), and 1 on the z-axis. The plane cuts the x-axis at the midpoint and the z-axis at the corner, remaining parallel to the y-axis.
2. (123) Plane: Take the reciprocals (1/1, 1/2, 1/3), resulting in intercepts at 1 on the x-axis, 0.5 on the y-axis, and 0.33 on the z-axis. The plane connects these three points on the respective axes of the unit cell.

The significance of these indices lies in their ability to describe the atomic arrangement on specific planes. Different planes have varying atomic packing densities, which directly influence the material's slip systems, plastic deformation behavior, chemical reactivity, and diffusion rates within the crystal lattice.