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Chapter 5: Problem 3

(a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.

Short Answer

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Short Answer: Interstitial and vacancy diffusion mechanisms involve the movement of atoms in a material. Interstitial diffusion occurs when small atoms move through interstitial spaces between lattice positions, while vacancy diffusion involves atoms moving between lattice positions via vacant sites. Interstitial diffusion is normally more rapid than vacancy diffusion due to the smaller size of the diffusing atoms which require less energy to move, and the higher availability of interstitial sites allowing more paths for diffusion.

Step by step solution

01

Define Interstitial and Vacancy Diffusion Mechanisms

Interstitial diffusion occurs when atoms move from one interstitial site (spaces between regular lattice positions) to another within the crystal structure of a material. These atoms are typically very small in size and can easily fit into the interstitial spaces without much disruption of the crystal lattice. Vacancy diffusion, on the other hand, occurs when atoms move from one lattice position to another via lattice vacancies. A vacancy is a vacant lattice site, where an atom has been removed from its original lattice position. In vacancy diffusion, atoms move by jumping into a nearby vacant site, effectively exchanging positions with the vacancy.
02

Comparing Interstitial and Vacancy Diffusion Mechanisms

While both interstitial and vacancy diffusion mechanisms involve the movement of atoms, they differ in the following ways: 1. In interstitial diffusion, atoms occupy the interstitial spaces, while in vacancy diffusion, they occupy the lattice sites. 2. Interstitial diffusion typically involves the movement of small atoms or ions within a crystal lattice, whereas vacancy diffusion involves the movement of lattice atoms themselves. 3. Interstitial diffusion generally does not cause any significant distortion of the crystal lattice, while vacancy diffusion may result in a slight change in the lattice arrangement.
03

Citing Reasons for the Faster Rate of Interstitial Diffusion

There are two main reasons why interstitial diffusion is generally more rapid than vacancy diffusion: 1. Small atom size: Interstitial diffusing atoms are typically much smaller than the lattice atoms, and therefore, they require less energy to move through the interstitial spaces of the lattice. This results in a higher diffusion coefficient for interstitial diffusion as compared to vacancy diffusion. 2. Higher availability of interstitial sites: Interstitial sites are often more abundant than vacancies in a crystal lattice, which allows interstitial diffusing atoms to have more paths available for diffusion. This results in a higher rate of diffusion for interstitial atoms compared to vacancy diffusion, where the movement relies on the limited availability of vacant lattice sites.

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Most popular questions from this chapter

The diffusion coefficients for silver in copper are given at two temperatures: $$ \begin{array}{cc} \hline T\left({ }^{\circ} \mathrm{C}\right) & D\left(\mathrm{~m}^{2} / \mathrm{s}\right) \\ \hline 650 & 5.5 \times 10^{-16} \\ 900 & 1.3 \times 10^{-13} \\ \hline \end{array} $$ (a) Determine the values of \(D_{0}\) and \(Q_{d}\). (b) What is the magnitude of \(D\) at \(875^{\circ} \mathrm{C}\) ?

The purification of hydrogen gas by diffusion through a palladium sheet was discussed in Section 5.3. Compute the number of kilograms of hydrogen that pass per hour through a 5-mm-thick sheet of palladium having an area of \(0.20 \mathrm{~m}^{2}\) at \(500^{\circ} \mathrm{C}\). Assume a diffusion coefficient of \(1.0 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}\), that the concentrations at the high- and low-pressure sides of the plate are \(2.4\) and \(0.6 \mathrm{~kg}\) of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.

The outer surface of a steel gear is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at \(850^{\circ} \mathrm{C}(1123 \mathrm{~K})\) for \(10 \mathrm{~min}\) increases the carbon concentration to \(0.90 \mathrm{wt} \%\) at a position \(1.0 \mathrm{~mm}\) below the surface. Estimate the diffusion time required at \(650^{\circ} \mathrm{C}(923 \mathrm{~K})\) to achieve this same concentration also at a) 1.0-mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. Use the diffusion data in Table \(5.2\) for C diffusion in \(\alpha\)-Fe.

Nitrogen from a gaseous phase is to be dif? fused into pure iron at \(700^{\circ} \mathrm{C}\). If the surface concentration is maintained at \(0.1 \mathrm{wt} \% \mathrm{~N}\) what will be the concentration \(1 \mathrm{~mm}\) from the surface after \(10 \mathrm{~h}\) ? The diffusion coefficient for nitrogen in iron at \(700^{\circ} \mathrm{C}\) is \(2.5 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).

The activation energy for the diffusion of carbon in chromium is \(111,000 \mathrm{~J} / \mathrm{mol}\). Calculate the diffusion coefficient at \(1100 \mathrm{~K}\left(827^{\circ} \mathrm{C}\right)\), given that \(D\) at \(1400 \mathrm{~K}\left(1127^{\circ} \mathrm{C}\right)\) is \(6.25 \times\) \(10^{-11} \mathrm{~m}^{2} / \mathrm{s}\)
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