ME Thermodynamics and Kinetics of Materials 2 — Questions and Answers
Question 1: The Arrhenius equation for a thermally activated process is k = A·exp(-Q/RT). What does Q represent?
- The pre-exponential frequency factor
- The activation energy for the process (Correct answer)
- The universal gas constant times temperature
- The equilibrium constant
Correct answer: The activation energy for the process
Q is the activation energy (in J/mol or eV/atom) representing the energy barrier that must be overcome for the process to occur.
Question 2: Fick's First Law of diffusion states that the diffusion flux J is related to the concentration gradient by:
- J = D (∂C/∂t)
- J = -D (∂C/∂x) (Correct answer)
- J = D (∂²C/∂x²)
- J = -D (∂²C/∂x²)
Correct answer: J = -D (∂C/∂x)
Fick's First Law is J = -D(∂C/∂x), where D is the diffusivity and the negative sign indicates flux from high to low concentration.
Question 3: A TTT (Time-Temperature-Transformation) diagram for a steel shows a 'nose' at intermediate temperatures. What does the nose represent?
- The fastest cooling rate to avoid martensite
- The temperature of maximum hardness
- The temperature at which transformation kinetics are fastest (Correct answer)
- The eutectoid temperature of the alloy
Correct answer: The temperature at which transformation kinetics are fastest
The nose of the TTT curve marks the temperature where the combined effect of undercooling (driving force) and atomic mobility produces the shortest transformation time.
Question 4: Homogeneous nucleation requires greater undercooling than heterogeneous nucleation because:
- Homogeneous nucleation releases more latent heat
- Heterogeneous nucleation on surfaces lowers the energy barrier by reducing the contact angle contribution (Correct answer)
- Homogeneous nucleation occurs at grain boundaries where energy is higher
- Heterogeneous nucleation requires more activation energy
Correct answer: Heterogeneous nucleation on surfaces lowers the energy barrier by reducing the contact angle contribution
Nucleation on pre-existing surfaces or particles reduces the surface energy term via the contact angle factor, lowering ΔG* compared to nucleation in a homogeneous melt.
Question 5: The Kirkendall effect in diffusion couples demonstrates that:
- Both species diffuse at the same rate in alloys
- Vacancies play no role in substitutional diffusion
- Different atomic species can have different intrinsic diffusion coefficients (Correct answer)
- Diffusion flux is always equal in both directions
Correct answer: Different atomic species can have different intrinsic diffusion coefficients
The Kirkendall effect (marker movement) proves that A and B atoms diffuse at different rates, requiring vacancy flux to balance the unequal atomic fluxes.
Question 6: The Avrami equation, f = 1 - exp(-kt^n), is used to describe isothermal phase transformation kinetics. The exponent n provides information about:
- The activation energy of the transformation
- The nucleation and growth mechanism (Correct answer)
- The equilibrium volume fraction of the product phase
- The diffusion coefficient of the slowest species
Correct answer: The nucleation and growth mechanism
The Avrami exponent n reflects the dimensionality of growth and whether nucleation is continuous or site-saturated, revealing the transformation mechanism.
Question 7: For diffusion of carbon in austenite (FCC iron), the diffusivity is higher than carbon in ferrite (BCC iron) at the same temperature primarily because:
- BCC iron has a lower melting point than FCC iron
- Austenite has larger octahedral interstitial sites relative to atom size (Correct answer)
- Carbon has a lower activation energy in BCC structures
- Ferrite has fewer grain boundaries for short-circuit diffusion
Correct answer: Austenite has larger octahedral interstitial sites relative to atom size
Although BCC has a more open structure overall, the octahedral interstitial site in FCC (austenite) is larger relative to the iron atom, accommodating carbon more easily and giving higher diffusivity.
ME Thermodynamics and Kinetics of Materials 2
The Arrhenius equation for a thermally activated process is k = A·exp(-Q/RT).
What does Q represent?