JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II THERMODYNAMICS OF MATERIALS Previous Question Paper (November/December - 2020 - R16)

Fick's laws describe the diffusion process in materials, relating the flux of diffusing species to the concentration gradient.

Fick's First Law states that the diffusion flux (J) is proportional to the concentration gradient (dc/dx) and is given by:

Here, D is the diffusion coefficient (diffusivity). The negative sign indicates that diffusion occurs from regions of high concentration to low concentration. This law applies to steady-state diffusion where the concentration profile does not change with time.

Fick's Second Law describes non-steady-state diffusion, where the concentration at a point changes over time. It is derived from the continuity equation and Fick's first law:

This law is essential for calculating concentration profiles in processes like carburization or homogenization, assuming D is independent of concentration.

Self-diffusion is the random movement of atoms within a pure material where the diffusing atoms are of the same type as the host lattice atoms. Since there is no chemical potential gradient, this process is driven by the minimization of Gibbs free energy through the random walk of atoms.

In pure metals, self-diffusion occurs primarily through vacancy mechanisms. Because atoms in a crystalline solid are tightly packed, they cannot move directly into adjacent sites. Instead, an atom jumps into an adjacent vacant lattice site (vacancy). This process is thermally activated, and the rate of diffusion depends on the concentration of vacancies and the frequency of atomic jumps.

The diffusion coefficient for self-diffusion follows the Arrhenius relationship:

Where D₀ is the pre-exponential factor, Q is the activation energy for self-diffusion (the sum of vacancy formation energy and vacancy migration energy), R is the gas constant, and T is the absolute temperature. As temperature increases, the concentration of vacancies increases exponentially, significantly enhancing the rate of self-diffusion.