JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III METALLURGY FOR NON METALLURGISTS Previous Question Paper (August - 2022 - R16)

The Atomic Packing Factor (APF) is a dimensionless ratio that quantifies the efficiency of atomic arrangement within a crystal structure. It is defined as the volume of atoms in a unit cell divided by the total volume of the unit cell.

Its importance lies in the following areas:

• Material Density: APF directly influences the theoretical density of a material. Higher packing factors generally correspond to denser materials, which is critical for structural applications.
• Plastic Deformation: The APF dictates the availability of slip systems. Structures with higher APF, such as Face-Centered Cubic (FCC) with an APF of 0.74, possess more slip systems, making them more ductile compared to structures with lower APF like Body-Centered Cubic (BCC) at 0.68.
• Diffusion: The amount of interstitial space, determined by the APF, influences the rate at which atoms can diffuse through the crystal lattice. Lower packing factors provide larger interstitial sites, facilitating easier diffusion.

Miller indices are a symbolic vector representation for the orientation of an atomic plane in a crystal lattice. The procedure to determine the indices (hkl) for a given plane is as follows:

1. Identify Intercepts: Determine the intercepts of the plane along the crystallographic axes (x, y, and z) in terms of unit cell dimensions. If the plane is parallel to an axis, the intercept is considered to be at infinity.
2. Take Reciprocals: Take the reciprocals of these intercepts. A value of infinity results in a reciprocal of zero.
3. Reduce to Smallest Integers: If the reciprocals are fractions, multiply them by a common factor to convert them into the smallest set of whole numbers.
4. Enclose in Parentheses: Write the resulting integers in parentheses as (hkl). Negative values are indicated by placing a bar over the number, such as (h k̄ l).

For example, if a plane intercepts the x-axis at 1, the y-axis at 1/2, and is parallel to the z-axis, the intercepts are (1, 1/2, ∞). The reciprocals are (1, 2, 0), resulting in the Miller indices (120).