Question

Which factor increases the rate of diffusion in solids?

• A. Lower temperature
• B. Higher temperature
• C. Higher atomic radius
• D. Presence of impurities

Hint:

An increase in temperature also exponentially increases the equilibrium concentration of vacancies in a crystalline solid, directly providing more paths for vacancy-assisted diffusion.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the factor that increases the rate of solid-state atomic diffusion.
Atomic diffusion in solid materials is the transport of mass by atomic motion.
Understanding diffusion kinetics is essential for several metallurgical heat treatments like carburizing, nitriding, and precipitation hardening.

Step 2: Key Formula or Approach:
The diffusion coefficient (\( D \)), which directly represents the rate of diffusion, is mathematically defined by the Arrhenius relation:
\[ D = D_0 \exp\left(-\frac{Q}{RT}\right) \]
where:
\( D \) is the diffusion coefficient,
\( D_0 \) is the pre-exponential constant,
\( Q \) is the activation energy for diffusion,
\( R \) is the universal gas constant, and
\( T \) is the absolute temperature in Kelvin.

Step 3: Detailed Explanation:

• Influence of Temperature: The temperature dependence of the diffusion coefficient is exponential.
With an increase in temperature, the kinetic energy of the atoms increases significantly, allowing a higher fraction of atoms to overcome the activation energy barrier (\( Q \)) and jump to adjacent vacancies or interstitial sites.
Therefore, a higher temperature drastically accelerates the rate of solid-state diffusion.

• Analysis of Other Options:
-

Lower temperature (Option A) reduces atomic vibrations and available thermal energy, thereby decreasing diffusion.
-

Higher atomic radius (Option C) makes atomic migration through interstitial or vacancy sites more difficult due to steric hindrance and lattice strain, which generally slows down the diffusion rate.
-

Presence of impurities (Option D) can sometimes impede the movement of other atoms by trapping them or causing local distortions, though its effect is less dominant and predictable than the direct exponential temperature influence.


Step 4: Final Answer:
Hence, higher temperature is the primary factor that increases the rate of diffusion in solids, matching Option (B).