# Phase Transformation Questions and Answers – Diffusion – High-Diffusivity Path

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This set of Phase Transformation Multiple Choice Questions & Answers (MCQs) focuses on “Diffusion – High-Diffusivity Path”.

1. In general, at any temperature the magnitudes of Db and Ds relative to the diffusivity through defect-free lattice D1 are such that_________ (Db and Ds are grain boundary and surface diffusivity)
a) Db>Ds>D1
b) Db<Ds<D1
c) Db>D1>Ds
d) Ds>Db>D1

Explanation: In general, at any temperature the magnitudes of Db and Ds relative to the diffusivity through defect-free lattice D1 are such that Ds>Db>D1. This mainly reflects the relative ease with which atoms can migrate along free surfaces, interior boundaries and through the lattice.

2. In an average metallic specimen the total grain boundary area is_______
a) Much greater than surface area
b) Same as the surface area
c) Relatively less than surface area
d) Much less than surface area

Explanation: Surface diffusion can play an important role in many metallurgical phenomena, but in an average metallic specimen the total grain boundary area is much greater than the surface area so that grain boundary diffusion is usually most important.

3. The fluxes of solute through the lattice J1 and along the boundary Jb are 3 and 4 mol/mm2sec. If the grain boundary has an effective thickness 2mm and the grain size is 2.5mm. Calculate the total flux?(In mol/mm2sec)
a) 6.2
b) 4.2
c) 3.2
d) 2.2

Explanation: The total flux is given by the equation (J1*α + Jb*β)/α, where α represents the grain size and β represent the effective thickness of grain boundary. So substituting the values in this equation we get the required solution that is (3*2+4*2.5)/2.5 = 6.2.
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4. In a diffusion couple made by welding together two metals, A and B.A-atoms diffusing along the boundary will be able to penetrate much deeper than atoms which only diffuse through the lattice.
a) True
b) False

Explanation: A-atoms diffusing along the boundary will be able to penetrate much deeper than atoms which only diffuse through the lattice. In addition, as the concentration of solute builds up in the boundaries, atoms will also diffuse from boundary into the lattice.

5. The diffusion through the lattice can be ignored under certain circumstances. Which among the following condition should be satisfied for the same if the diffusivity through a defect free lattice is given as 2.5 mm2/sec and the grain size is given as 5mm? (Consider the diffusivity through the grain boundary as 2mm2/sec)
a) When the effective thickness of grain boundary is 6.25mm
b) When the effective thickness of grain boundary is 1000mm
c) When the effective thickness of grain boundary is 0.001mm
d) When the effective thickness of grain boundary is 10mm

Explanation: In this case 2*1000>>2.5*5. It can be seen that the relative importance of lattice and grain boundary diffusion depends on the ratio Db*ȣ/ D1*d. When Db*ȣ>>D1*d, diffusion through the lattice can be ignored in comparison to grain boundary diffusion.(Db and D1 are the diffusivities through the grain boundary and defect free lattice and ȣ, d are the effective thickneβ and grain size).

6. The relative magnitudes of Db*ȣ and D1*d are most sensitive to_______(Where Db and D1 are the diffusivities through the grain boundary and defect free lattice and ȣ, d are the effective thickness and grain size)
a) Pressure
b) Temperature
c) Volume
d) Composition

Explanation: The relative magnitudes of Db*ȣ and D1*d are most sensitive to temperature. Note that although Db > Dȣ, at all temperatures, the difference increases as temperature decreases. This is because the activation energy for diffusion along grain boundaries (Qb) is lower than that for lattice diffusion (Q1).

7. The jump frequency for atoms migrating along the defects is higher than that for diffusion in the lattice.
a) True
b) False

Explanation: It can be shown experimentally that the jump frequency for atoms migrating along these defects is higher than that for diffusion in the lattice. It will become apparent that under certain circumstances diffusion along these defects can be the dominant diffusion path.

8. In FCC metals it is generally found that ___
a) Qb >> 0.5Q1
b) Qb << 0.5Q1
c) Qb = Q1
d) Qb ̴̴ Q1

Explanation: This means that when the grain boundary diffusivity is scaled by the factor ȣ/d the grain boundary contribution to the total, or apparent, diffusion coefficient is negligible in comparison to the lattice diffusivity at high temperatures, but dominates at low temperatures.

9. The rate at which atoms diffuse along different boundaries is_________
a) Same
b) Different
c) Constant
d) Cannot be predicted

Explanation: The rate at which atoms diffuse along different boundaries is not the same, but depends on the atomic structure of the individual boundary. This in turn depends on the orientation of the adjoining crystals and the plane of the boundary. Also, the diffusion coefficient can vary with direction within a given boundary plane (ȣ, d is the effective thickneβ and grain size).

10. The dislocations effectively act as pipes along which atoms can diffuse with a diffusion coefficient 2.5mm2/sec. Calculate the apparent diffusivity if the cross-sectional area of pipe per unit area of matrix is given as 10-1? (If D1 (diffusivity through defect free lattice) is given as 5mm2/sec)
a) 5.45 mm2/sec
b) 5.25 mm2/sec
c) 6.35 mm2/sec
d) 5.75 mm2/sec

Explanation: It can easily be shown that the apparent diffusivity through a single crystal containing dislocations, Dapp, is related to the lattice diffusion coefficient by Dapp=D1 (1+g*(Dp/D1)), where g is the cross-sectional area of ‘pipe’ per unit area of matrix. The contribution of dislocations to the total diffusive flux through a metal will of course depend on the relative cross-sectional areas of pipe and matrix.

11. Find the frequency factor of the following grain boundary diffusion, if the activation energy is given as 90KJ/mol and the diffusivity at the grain boundary at 1071K is given as 49*10-6m2/sec?
a) 1.2mm2/sec
b) 1.2m2/sec
c) 2.2mm2/sec
d) 4.2mm2/sec

Explanation: It is found experimentally that diffusion along grain boundaries and free surfaces can be described by Db=Db’*exp (-Qb/RT), where Db the grain boundary diffusivity and Db’ the frequency factor. Qb is the experimentally determined values of the activation energy for diffusion. So in this case substituting the respective values we get, Db = 49*10-6*exp (-90000/R*1071) =1.2mm2/sec.

12. At high temperatures diffusion through the lattice is rapid and g*Dp / D1 is very small so that the dislocation contribution to the total flux of atoms is_______ (Dp, D1 are diffusivity through pipe and defect free lattice and g is the cross-sectional area of ‘pipe’ per unit area of matrix).
a) Extremely high
b) Negligible
c) Low
d) High

Explanation: The total flux of atoms will be negligible. But it is found that the activation energy in lattice diffusion is higher than that of pipe diffusion. D1 decreases more rapidly than Dp and this happens with the decrease in temperature.

13. Grain boundary diffusion makes a significant contribution to the total flux when___(Db and D1 are the diffusivities through the grain boundary and defect free lattice and ȣ, d are the effective thickneβ and grain size).
a) (Db*ȣ/D1*d) > 1
b) (Db*ȣ/D1*d) < 1
c) (Db*ȣ/D1*d) = 1
d) (Db*ȣ/D1*d) < 0

Explanation: Grain boundary diffusion makes a significant contribution to the total flux when the following condition is satisfied, Db*ȣ> D1*d. The effective width of a grain boundary in many cases is 0.5nm. Grain sizes on the other hand can vary from ̴ 1 to 1000 (10-6m) and the effectiveneβ of the grain boundaries will vary accordingly.

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