(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: Interstitial and vacancy diffusion are two mechanisms for atomic diffusion in solid materials. Interstitial diffusion occurs when atoms or molecules move through the interstitial sites of the crystal lattice structure, while vacancy diffusion involves atoms moving from one lattice site to another vacant site. Interstitial diffusion is generally more rapid than vacancy diffusion because interstitial atoms/ions are smaller in size, allowing for easier movement through the lattice and requiring less energy for atomic migration. Additionally, there are more interstitial spaces available within a crystal lattice compared to the number of vacancies, contributing to the higher diffusion rate for interstitial diffusion.

Step by step solution

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A. Definitions

Interstitial diffusion and vacancy diffusion are two mechanisms for atomic diffusion in solid materials. 1. Interstitial diffusion: In this mechanism, diffusion occurs when atoms or molecules move through the interstitial sites of the crystal lattice structure. It means that the atoms or molecules pass through the empty spaces between the already existing atoms in the lattice. 2. Vacancy diffusion: In vacancy diffusion, atoms move from one lattice site to another vacant site by relocating vacancies. A vacancy is an empty lattice site within the crystal structure where an atom should be present but is missing.
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B. Comparison of the mechanisms

Interstitial and vacancy diffusion mechanisms can be compared in terms of their atomic movement and diffusion rates. 1. Atomic movement: In interstitial diffusion, an atom or molecule moves through the empty spaces within the crystal lattice, while in vacancy diffusion, the atom moves from one lattice site to another vacant site by swapping positions with the vacancy. 2. Diffusion rates: The diffusion rate for interstitial diffusion is generally faster than that of vacancy diffusion. This difference in diffusion rate is due to the atomic movement and the availability of spaces for atomic motion.
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C. Reasons for the rapid interstitial diffusion

There are two main reasons why interstitial diffusion is often more rapid than vacancy diffusion: 1. Interstitial atoms/ions are smaller in size: The interstitial atoms or molecules are generally of smaller size compared to the atoms in the crystal lattice. The smaller atom/ion size allows them to easily move through the interstitial spaces compared to the vacancies, which need to be large enough to accommodate an atom/ion to initiate vacancy diffusion. Thus, interstitial diffusion requires less energy for atomic migration. 2. Greater availability of interstitial spaces: There are generally more interstitial spaces available within a crystal lattice compared to the number of vacancies. This greater availability of sites for diffusion contributes to the higher diffusion rate for interstitial diffusion.

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Most popular questions from this chapter

An FCC iron-carbon alloy initially containing 0.10 wt \(\% \mathrm{C}\) is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.10 wt\%. If after 48 h the concentration of carbon is \(0.30 \mathrm{wt} \%\) at a position \(3.5 \mathrm{mm}\) below the surface, determine the temperature at which the treatment was carried out.

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Consider a diffusion couple composed of two semi-infinite solids of the same metal, and that each side of the diffusion couple has a different concentration of the same elemental impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion couple. For this situation, the solution to Fick's second law (assuming that the diffusion coefficient for the impurity is independent of concentration), is as follows: $$C_{x}=\left(\frac{C_{1}+C_{2}}{2}\right)-\left(\frac{C_{1}-C_{2}}{2}\right) \operatorname{erf}\left(\frac{x}{2 \sqrt{D t}}\right).$$In this expression, when the \(x=0\) position is taken as the initial diffusion couple interface, then \(C_{1}\) is the impurity concentration for \(x<0\) likewise, \(C_{2}\) is the impurity content for \(x>0\).A diffusion couple composed of two platinum-gold alloys is formed; these alloys have compositions of \(99.0 \mathrm{wt} \% \mathrm{Pt}-1.0 \mathrm{wt} \%\) Au and 96.0 wt \(\%\) Pt- 4.0 wt\% Au. Determine the time this diffusion couple must be heated at \(1000^{\circ} \mathrm{C}(1273 \mathrm{K})\) in order for the composition to be 2.8 wt \(\%\) Au at the \(10 \mu \mathrm{m}\) position into the \(4.0 \mathrm{wt} \%\) Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in \(\mathrm{Pt}\) are \(1.3 \times 10^{-5}\) \(\mathrm{m}^{2} / \mathrm{s}\) and \(252,000 \mathrm{J} / \mathrm{mol},\) 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 h? The diffusion coefficient for nitrogen in iron at \(675^{\circ} \mathrm{C}\) is \(1.9 \times 10^{-11} \mathrm{m}^{2} / \mathrm{s}\).

Self-diffusion involves the motion of atoms that are all of the same type; therefore it is not subject to observation by compositional changes, as with inter-diffusion. Suggest one way in which self-diffusion may be monitored.

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