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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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Answer: Two main reasons why interstitial diffusion is generally faster than vacancy diffusion are: 1) atoms involved in interstitial diffusion are generally smaller, allowing them to easily move through interstitial sites, and 2) interstitial diffusion requires a lower energy barrier for movement, as atoms do not need to physically swap positions with other atoms like in vacancy diffusion, leading to a faster diffusion process.

Step by step solution

01

Define Interstitial Diffusion

Interstitial diffusion is a diffusion process in which atoms or molecules migrate through a lattice by moving from one interstitial site to another. The interstitial sites are spaces between the main lattice points where the migrating atom or molecule can fit.
02

Define Vacancy Diffusion

Vacancy diffusion is a diffusion process in which atoms or molecules exchange positions with vacancies, or empty lattice points, allowing them to move within the lattice structure. This movement generally requires atoms to physically swap positions, and requires more energy to be applied in order to overcome the potential energy barrier of doing so.
03

Compare Interstitial and Vacancy Diffusion

In interstitial diffusion, the atoms or molecules travel in the open spaces between the atoms of the host lattice structure, whereas in vacancy diffusion, the diffusing elements move by exchanging positions with an adjacent vacancy in the lattice structure. Because the two mechanisms involve different paths for atomic movement, their rate and ease of diffusion can differ greatly.
04

Describe Reason 1 for Interstitial Diffusion being more rapid

One reason for interstitial diffusion being more rapid than vacancy diffusion is that the atoms or molecules involved are generally smaller than the host lattice atoms. Due to their smaller size, they can easily move through the interstitial sites, while in vacancy diffusion, the migrating atoms need to be nearly the same size as the host lattice atoms to successfully exchange positions with vacancies. The larger the atom to move, the more energy is required and the slower the diffusion process.
05

Describe Reason 2 for Interstitial Diffusion being more rapid

Another reason why interstitial diffusion is generally faster is that it requires a lower energy barrier for movement, as the migrating atoms do not need to physically swap positions with other atoms, unlike vacancy diffusion. The energy barrier in vacancy diffusion is the energy required for an atom to move out of its initial position and into an adjacent vacancy, whereas, in interstitial diffusion, atoms simply move between the spaces in the lattice, requiring less energy input. Less energy to overcome the energy barrier leads to a faster diffusion process.

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Most popular questions from this chapter

When \(\alpha\)-iron is subjected to an atmosphere of ( nitrogen gas, the concentration of nitrogen in the iron, \(C_{\mathrm{N}}\) (in weight percent), is a function of hydrogen pressure, \(p_{\mathrm{N}_{2}}\) (in \(\left.\mathrm{MPa}\right)\), and absolute temperature \((T)\) according to $$ C_{\mathrm{N}}=4.90 \times 10^{-3} \sqrt{p_{\mathrm{N}_{2}}} \exp \left(-\frac{37,600 \mathrm{~J} / \mathrm{mol}}{R T}\right) $$ Furthermore, the values of \(D_{0}\) and \(Q_{d}\) for this diffusion system are \(5.0 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) and \(77,000 \mathrm{~J} / \mathrm{mol}\), respectively. Consider a thin iron membrane 1.5-mm thick at \(300^{\circ} \mathrm{C}\). Compute the diffusion flux through this membrane if the nitrogen pressure on one side of the membrane is \(0.10 \mathrm{MPa}(0.99 \mathrm{~atm})\) and on the

Consider a diffusion couple composed of two cobalt-iron alloys; one has a composition of \(75 \mathrm{wt} \%\) Co-25 wt\% Fe; the other alloy composition is \(50 \mathrm{wt} \%\) Co-50 wt \(\% \mathrm{Fe}\). If this couple is heated to a temperature of \(800^{\circ} \mathrm{C}(1073 \mathrm{~K})\) for \(20,000 \mathrm{~s}\) determine how far from the original interface into the \(50 \mathrm{wt} \%\) Co-50 wt \% Fe alloy the composition has increased to \(52 \mathrm{wt} \%\) Co-48 wt Fe. For the diffusion coefficient, assume values of \(6.6 \times 10^{-t}\) \(\mathrm{m}^{2} / \mathrm{s}\) and \(247,000 \mathrm{~J} / \mathrm{mol}\), respectively, for the pre exponential and activation energy.

Carbon is allowed to diffuse through a steel plate 10 -mm thick. The concentrations of carbon at the two faces are \(0.85\) and \(0.40 \mathrm{~kg} \mathrm{C} / \mathrm{cm}^{3} \mathrm{Fe}\), which are maintained constant. If the preexponential and activation energy are \(5.0 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) and 77,000 \(\mathrm{J} / \mathrm{mol}\), respectively, compute the temperature at which the diffusion flux is \(6.3 \times 10^{-10} \mathrm{~kg} / \mathrm{m}^{2} \mathrm{~s}\).

For the predeposition heat treatment of a semiconducting device, gallium atoms are to be diffused into silicon at a temperature of \(1150^{\circ} \mathrm{C}\) for \(2.5 \mathrm{~h}\). If the required concentration of \(\mathrm{Ga}\) at a position \(2 \mu \mathrm{m}\) below the surface is \(8 \times 10^{23}\) atoms \(/ \mathrm{m}^{3}\), compute the required surface concentration of \(\mathrm{Ga}\). Assume the following: (i) The surface concentration remains constant (ii) The background concentration is \(2 \times 10^{19} \mathrm{Ga}\) atoms \(/ \mathrm{m}^{3}\) (iii) Preexponential and activation energy values are \(3.74 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\) and \(3.39 \mathrm{eV} /\) atom, respectively.

Nitrogen from a gaseous phase is to be diffused into pure iron at \(675^{\circ} \mathrm{C}\). If the surface concentration is maintained at \(0.2 \mathrm{wt} \% \mathrm{~N}\), what will be the concentration \(2 \mathrm{~mm}\) from the surface after \(25 \mathrm{~h}\) ? The diffusion coefficient for nitrogen in iron at \(675^{\circ} \mathrm{C}\) is \(2.8 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).
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