# Powder Metallurgy Questions and Answers – Sintering Mechanism – 1

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This set of Powder Metallurgy Multiple Choice Questions & Answers (MCQs) focuses on “Sintering Mechanism – 1”.

1. Which of the following are the main types of material transport mechanisms proposed to be operating during sintering?
a) Evaporation
b) Dislocation movement
c) Evaporation-condensation, viscous flow, plastic flow and diffusion
d) Viscous flow, metal flow

Explanation: A number of material transport mechanisms have been proposed to be operating during sintering. These are, (1) Evaporation and condensation, (2) Viscous flow, (3) Plastic flow, and (4) Diffusion (volume diffusion, grain boundary diffusion, and surface diffusion).

2. _______ is the ‘liquid-like’ movement of individual atoms under stress while _______ is the slip of entire planes of atoms.
a) Plastic flow, viscous flow
b) Volume diffusion, plastic flow
c) Viscous flow, volume diffusion
d) Viscous flow, plastic flow

Explanation: Viscous flow is the ‘liquid-like’ movement of individual atoms under stress while the plastic flow is the dislocation movement or the slip of entire planes of atoms.

3. ________ mechanism operates in a system having materials with a high vapor pressure at sintering temperature.
a) Viscous flow
b) Volume diffusion
c) Evaporation and condensation
d) Plastic flow

Explanation: Evaporation and condensation is a simple mechanism, which operates in a system having materials with a high vapor pressure at the sintering temperatures. Evaporation-condensation is driven by pressure differences created by surface curvature and changes the shape of the particles and pores.

4. The driving force for evaporation-condensation mechanism is given by ________
a) μ-μ0=(γΩ)/r1=RT ln$$\frac{p_0}{p}$$
b) μ-μ0=(-γΩ)/r1=RT ln$$\frac{p}{p_0}$$
c) μ0-μ=(-γΩ)/r1=RT ln$$\frac{p}{p_0}$$
d) μ-μ0=(γΩ)/r1=RT ln$$\frac{p}{p_0}$$

Explanation: Based on the Gibbs-Thomson equation, the driving force for the evaporation-condensation mechanism is given by μ-μ0=(-γΩ)/r1=RT ln$$\frac{p}{p_0}$$ where μ0 and μ are chemical potentials of initial and final surfaces, R is the universal gas constant, T is the temperature in Kelvin and p and p0 are the partial pressures over the curved (under stress) surface and flat (stress-free) surface respectively, γ is the surface energy and Ω is the atomic volume.

5. The mass transport during evaporation-condensation mechanism occurs from _______ particle surface to the ______ necks.
a) Concave, convex
b) Convex, bi-concave
c) Convex, concave
d) Bi-convex, concave

Explanation: The mass transport during the evaporation-condensation mechanism occurs from the flat surface to the stressed region (or) from the convex particle surface to the concave necks. The rate of transfer of materials depends on the vapor pressure gradient between the two surfaces as well as the rate of evaporation.

6. The equilibrium vapor pressure over the neck _____ particle surface.
a) <
b) >
c) =
d) >>

Explanation: The equilibrium vapor pressure over a concave surface (i.e. neck or pore) is lower compared to that of a convex surface (i.e. particle surfaces), resulting in mass transport along the vapor pressure gradient, from the convex surfaces to the concave necks and the driving force for this mechanism is the surface tension force, which gives rise to stresses in the green compact.

7. Diffusion occurs as a result of _______ gradient.
a) Velocity
b) Vacancy concentration
c) Pressure
d) Momentum

Explanation: The vacancy concentration gradient is the reason for the diffusion process to occur. This vacancy concentration depends on temperature and chemical potential gradient which occurs due to stress acting on the metal surface.

8. Vacancy concentration causes _______
a) The outflow of vacancies from the curved surface towards the flat region
b) The outflow of vacancies from the flat surface towards the curved region
c) The outflow of atoms from the curved surface towards the flat region
d) The influx of vacancies from the curved surface towards the flat region

Explanation: Vacancy concentration gradient (C-C0) is given by the equation-
(C- C0)=γΩC0/r(RT)
Vacancy concentration gradient (C-C0) causes an outflow of vacancies from the curved surface towards the flat surface and an influx of atoms in the opposite direction.

9. The vacancy concentration is given by Dvac= ______
a) D.C0
b) D.C
c) d.C
d) D.c

Explanation: If the volume of the material is D and the vacancy concentration is Dvac in the material are known, then Dvac=D.C0. The vacancy concentration C0 causes movement of vacancies from the neck region leading to neck growth.

10. What is the empirical relationship for the rate of neck growth when a sphere is in contact with a flat surface?
a) Rate of neck growth ∝ $$t^{\frac{1}{6}}$$
b) Rate of neck growth ∝ $$t^{\frac{1}{7}}$$
c) Rate of neck growth ∝ $$t^{\frac{2}{7}}$$
d) Rate of neck growth ∝ $$t^{\frac{1}{8}}$$

Explanation: The empirical relationship for the rate of neck growth when a sphere is in contact with a flat surface is given by- Rate of neck growth ∝ $$t^{\frac{1}{7}}$$ where t is time. In this case, material transport occurs by diffusion of vacancies away from the neck region and movement of atoms from a flat surface into neck region (i.e. surface diffusion).

11. What is the empirical relationship for the rate of neck growth when two spheres are in contact with one another?
a) $$\frac{x^7}{a^4}=\frac{40\gamma \Omega D.t}{RT}$$
b) $$\frac{a^2}{x^5}=\frac{400 \gamma \Omega D.t}{RT}$$
c) $$\frac{x^5}{a^2}=\frac{40\gamma\Omega D.t}{RT}$$
d) $$\frac{x^5}{a^3}=\frac{40\gamma \Omega D.t}{RT}$$
Explanation: When two spheres are in contact with one another, the rate of neck growth between the two spheres is given by the equation- $$\frac{x^5}{a^2}=\frac{40\gamma \Omega D.t}{RT}$$ where x=neck radius (m), a=radius of the sphere (m), t is time (sec), γ is the surface energy, D is the diffusivity of the material and Ω is the atomic or molecular volume.