# Powder Metallurgy Questions and Answers – Sintering Mechanism – 2

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This set of Powder Metallurgy Interview Questions and Answers for freshers focuses on “Sintering Mechanism – 2”.

1. Which of the following transport mechanisms can occur for two spheres in contact with one another during sintering?
a) Evaporation-condensation, surface diffusion and volume diffusion
b) Evaporation-condensation, surface diffusion, volume diffusion, volume diffusion of vacancies, and grain boundary diffusion
c) Surface diffusion
d) Volume diffusion

Explanation: For two spheres in contact with one another during sintering following transport mechanisms can occur. (1) Evaporation and condensation, (2) Material transport from the flat surface to the neck through surface diffusion, (3) Volume diffusion from flat surface to the neck, and (4) Volume diffusion of vacancies from neck (under tensile stress) to the neck through the grain boundaries which are under compressive stress and vacancy flow through grain boundaries to the neck region by grain boundary diffusion.

2. Neck growth rate due to surface diffusion from the surface source is R1= _______
a) 2Dsδs$$FK_{1}^3$$
b) 2Dsδs$$FK_{3}^1$$
c) 2Ds$$FK_{1}^3$$
d) 2Dsδs$$FK_{1}^4$$

Explanation: Neck growth rate due to surface diffusion from the surface source is R1=2Dsδs$$FK_{1}^3$$ where, R1=rate of neck growth for surface diffusion, F=$$\frac{\Omega \gamma_s}{kT}$$, K1=curvature difference, which drives the diffusive fluxes, Ds=surface diffusion coefficient, δs=effective surface thickness, γs=surface free energy, Ω=atomic or molecular volume, and k=Boltzmann constant.

3. Neck growth rate due to lattice diffusion from the surface source is R2= _______
a) 2Ds$$FK_{1}^3$$
b) 2Ds$$FK_{1}^2$$
c) 2Dv$$FK_{1}^3$$
d) 2Dv$$FK_{1}^2$$

Explanation: Neck growth rate due to lattice diffusion from the surface source is R2=2Dv$$FK_{1}^2$$, where Dv=lattice diffusion coefficient, , F=$$\frac{\Omega \gamma_s}{kT}$$, K1=curvature difference, γs=surface free energy, Ω=atomic or molecular volume, and k=Boltzmann constant.
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4. The empirical relationship for neck growth rate due to vapor transport from the surface source is R3= _______
a) PvFK1$$\sqrt{\frac{\Omega}{2\pi \rho_{0}kT}}$$
b) PvFK1$$\sqrt{\frac{\Omega}{2\pi \rho_{0}T}}$$
c) PvFK1$$\sqrt{\frac{\Omega}{2\rho_{0}kT}}$$
d) PvFK1$$\sqrt{\frac{\Omega T}{2\pi \rho_{0}k}}$$

Explanation: The empirical relationship for neck growth rate due to vapor transport from the surface source is R3=PvFK1$$\sqrt{\frac{\Omega}{2\pi \rho_{0}kT}}$$ where, Pv=vapor pressure, ρ0=theoretical density, F=$$\frac{\Omega \gamma_s}{kT}$$, K1=curvature difference, γs=surface free energy, Ω=atomic or molecular volume, and k=Boltzmann constant.

5. The empirical relationship for neck growth rate due to grain boundary transport from sources on the grain boundary is R4= _______
a) 4DBδB$$FK_{2}^1$$/x
b) 4DBδB$$FK_{2}^1$$/x2
c) 4DBδB$$FK_{2}^1$$/a
d) 4DBδB$$FK_{2}^2$$/x

Explanation: The empirical relationship for neck growth rate due to grain boundary transport from sources on the grain boundary is R4=4DBδB$$FK_{2}^2$$/x, where DB=grain boundary diffusion coefficient, δB=effective grain boundary thickness, F=$$\frac{\Omega \gamma_s}{kT}$$, γs=surface free energy, Ω=atomic or molecular volume, x=neck radius, and k=Boltzmann constant.

6. Neck growth rate due to lattice diffusion from sources on the grain boundary is R5= _______
a) 2Dv$$FK_{1}^2$$
b) 2Dv$$FK_{1}^3$$
c) 4Dv$$FK_{1}^2$$
d) 4Dv$$FK_{2}^2$$

Explanation: The empirical relationship for neck growth rate due to lattice diffusion from sources on the grain boundary is R5=4Dv$$FK_{2}^2$$ where, Dv=lattice diffusion coefficient, F=$$\frac{\Omega \gamma_s}{kT}$$, γs=surface free energy, Ω=atomic or molecular volume, and k=Boltzmann constant.

7. The empirical relationship for neck growth rate due to lattice diffusion from dislocation sources is R6= _______,
a) $$\Big(\frac{4}{9}\Big)$$K2Nx2DvF(K2–$$\frac{2\epsilon x}{3\gamma_sa})$$
b) $$\Big(\frac{4}{9}\Big)$$Nx2DvF(K2–$$\frac{3\epsilon x}{2\gamma_sa})$$
c) $$\Big(\frac{4}{9}\Big)$$K2Nx2DvF(K2–$$\frac{3\epsilon x}{2\gamma_sa})$$
d) $$\Big(\frac{4}{9}\Big)$$K2Nx2Dv(K2–$$\frac{3\epsilon x}{2\gamma_sa})$$

Explanation: The empirical relationship for neck growth rate due to lattice diffusion from dislocation sources is R6=$$\Big(\frac{4}{9}\Big)K_2Nx^2D_vF(K_2-\frac{3\epsilon x}{2\gamma_sa})$$ where, N=dislocation density, ε=shear modulus, F=$$\frac{\Omega \gamma_s}{kT}$$, γs=surface free energy, Ω=atomic or molecular volume, x=neck radius, a=radius of the sphere, and k=Boltzmann constant.

8. Which of the following mechanism does not lead to shrinkage?
a) Viscous flow
b) Surface diffusion
c) Volume diffusion
d) Grain boundary diffusion

Explanation: Out of the various mechanisms for sintering only viscous flow, plastic flow, volume diffusion, and grain boundary diffusion can lead to shrinkage. Surface diffusion and evaporation-condensation do not lead to shrinkage.

9. ________ mechanism alters the shape of the neck and particle surface.
a) Viscous flow
b) Volume diffusion
c) Evaporation-condensation
d) Plastic flow

Explanation: Evaporation-condensation and surface diffusion do not lead to shrinkage but do alter the shape of the neck and particle surface by redistribution of atoms as they reach the surface of the neck.

10. The expression for the number of vacant site N is given by ________
a) N=N0$$e^{\frac{-Q}{RT}}$$
b) N=N0$$e^{\frac{-Qt}{RT}}$$
c) N=N0$$e^{\frac{-QT}{R}}$$
d) N=N0$$e^{\frac{Q}{RT}}$$

Explanation: Sintering involves the movement of atoms and hence a large number of high energized atoms along with a sufficient number of vacant sites (N) must be available for sintering to take place. This is represented by Arrhenius relation, N=N0$$e^{\frac{-Q}{RT}}$$ where, N0 is the total number of lattice sites, R is the universal gas constant, and Q is the activation energy for transport.

11. According to ______, there are six stages of sintering.
a) Schroter
b) Nabarro and Herring
c) Kuczynsky
d) Hutteg

Explanation: According to Hutteg, there are six stages of sintering for different increasing temperature regions that correspond to the dominance of different mechanisms such as adhesion along with particle rearrangement, surface diffusion, grain growth, lattice diffusion, recrystallization, and excessive grain growth respectively.

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