Module-5-Diffusion

Chapter 5: Diffusion

Overview of Diffusion

• Diffusion is the process by which particles move from an area of high concentration to an area of low concentration.

Diffusion Mechanisms

• Interstitial Diffusion: Occurs when impurity atoms occupy interstitial sites (spaces between lattice atoms).

• Substitutional Diffusion: Involves impurity atoms substituting for atoms in the crystal lattice.

Types of Diffusion

Steady State vs Non-Steady State

• Steady State Diffusion:

  • The flux of atoms is constant over time.

  • Conditions: dc/dx = constant, dc/dt = 0.

• Non-Steady State Diffusion:

  • The flux is time-dependent, with changes in concentration over time.

  • Conditions: dc/dx varies with time, dc/dt ≠ 0.

  • Governed by Fick’s laws of diffusion:

    • Fick's First Law: Applies to both steady and non-steady state diffusion.

    • Fick's Second Law: Specific to non-steady state diffusion.

Steady-State Diffusion

• Defined whereby the diffusion flux remains unchanged over time.

• Key factors include:

  • Concentration profile of diffusing species.

  • Concentration gradient (dc/dx) dictates the pace of diffusion.

Equation for Steady-State Diffusion

• Fick's First Law: [ J = -D \frac{dC}{dx} ]

  • Where D is the diffusion coefficient and J is the flux of atoms across an area A.

  • The negative sign indicates movement down the concentration gradient.

Non-Steady-State Diffusion

• Described by Fick's Second Law: [ D \frac{d^2C}{dx^2} = \frac{\partial C}{\partial t} ]

  • Involves time-dependent changes in concentration profile.

Factors Influencing Diffusion

1. Diffusing Species:

   • Rates vary based on the species and the host material (e.g., self-diffusion vs. carbon inter-diffusion in iron).

2. Temperature:

   • Diffusion coefficient increases with temperature, described by: [ D = D_0 ext{exp}(-\frac{Q_d}{RT}) ]

   • (D_0): temperature-independent pre-exponential;(Q_d): activation energy for diffusion.

   • Arrhenius plots can be used to determine Do and Q.

3. Interstitial and Vacancy Diffusion Mechanisms:

   • Smaller diffusing atoms (e.g., H, C) diffuse faster than larger atoms.

4. Role of Microstructure:

   • Diffusion rates differ based on structural regions like grain boundaries and dislocations.

Examples of Diffusion Mechanisms

• Self-Diffusion: Atoms in the same phase move throughout the lattice.

• Particular examples of diffusion coefficients for different species show considerable variation dependent on atomic size and structure.

Non-Equilibrium Transformation & Microstructure

• Coring: Gradual compositional changes within grains; often removed through annealing.

• Segregation: Concentration of impurities along grain boundaries; impacts the quality of alloys.

• Micro-segregation: Differences in composition across crystals; can often be corrected.

• Macro-segregation: Larger compositional variations that persist after processing.

Conclusions

• Understanding diffusion mechanisms is essential for materials engineering, affecting alloy design, property control, and various engineering applications.