Briefly explain the concept of steady state as it applies to diffusion.

Short Answer

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Answer: In diffusion, the significance of steady state lies in the fact that it represents a dynamic equilibrium where the concentration gradient remains constant over time, and the net flux of particles between regions is zero. This allows us to predict the final outcome of the diffusion process in terms of concentration profiles and understand the system's response to changes in external factors. Furthermore, it has practical implications in various fields of science and engineering for designing efficient processes and optimizing the performance of devices.

Step by step solution

01

Define Diffusion

Diffusion is the process by which particles move from an area of higher concentration to an area of lower concentration, resulting in the eventual equilibrium of the concentrations. This process is driven by the random motion of particles and is typically described using Fick's Laws.
02

Introduce the Concept of Steady State

A steady state is a situation in which certain key variables in a system remain constant over time, even though the individual components of the system may be changing. In other words, the system is in a state of dynamic equilibrium, where any changes that occur are balanced out by opposing changes, so the overall state of the system remains stable. Since diffusion moves particles from regions of higher to lower concentrations, a steady state can be reached if the concentration gradient remains constant.
03

Explain the Significance of Steady State in Diffusion

In the context of diffusion, a steady state occurs when the rate at which particles are moving from one region to another is balanced by the reverse process, which means the concentration gradient remains constant over time. When a system reaches a steady state, the net flux of particles between the regions is zero. It is important to note that reaching a steady state does not mean that the diffusion process has stopped; rather, the opposing processes responsible for the concentration gradient are balanced, so the overall concentration profile in the system remains constant.
04

Implications of Steady State in Diffusion

The steady state condition in diffusion provides valuable information about the behavior of the system. Knowing the steady state conditions allows us to predict the final outcome of the diffusion process in terms of concentration profiles, while also giving insights into the system's response to changes in external factors such as temperature or pressure. In engineering and scientific applications, understanding the steady state properties of a system can help in designing efficient processes, controlling the transport of materials, and optimizing the performance of various devices. In conclusion, the concept of a steady state in diffusion refers to a state where the concentration gradient remains constant over time, and the net flux of particles between regions is zero. This dynamic equilibrium provides valuable information about the behavior of the system and has practical implications in various fields of science and engineering.

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Most popular questions from this chapter

At approximately what temperature would a specimen of \(\gamma\)-iron have to be carburized for \(2 \mathrm{~h}\) to produce the same diffusion result as at \(900^{\circ} \mathrm{C}\) for \(15 \mathrm{~h}\) ?

(a) Briefly explain the concept of a driving force. (b) What is the driving force for steady-state diffusion?

An FCC iron-carbon alloy initially containing \(0.35 \mathrm{wt} \% \mathrm{C}\) is exposed to an oxygen-rich and virtually carbon-free atmosphere at \(1400 \mathrm{~K}\) (1127 \(\left.^{\circ} \mathrm{C}\right)\). Under these circumstances the carbon diffuses from the alloy and reacts at the surface, with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at \(0 \mathrm{wt} \%\) C. (This process of carbon depletion is termed decarburization.) At what position will the carbon concentration be \(0.15 \mathrm{wt} \%\) after a 10 -h treatment? The value of \(D\) at \(1400 \mathrm{~K}\) is \(6.9 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).

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 silver-gold alloys is formed; these alloys have compositions of \(98 \mathrm{wt} \% \mathrm{Ag}-2 \mathrm{wt} \% \mathrm{Au}\) and \(95 \mathrm{wt} \% \mathrm{Ag}-5 \mathrm{wt} \%\) Au. Determine the time this diffusion couple must be heated at \(750^{\circ} \mathrm{C}\) (1023 K) in order for the composition to be \(2.5 \mathrm{wt} \% \mathrm{Au}\) at the \(50 \mu \mathrm{m}\) position into the 2 wt \(\%\) Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in \(\mathrm{Ag}\) are \(8.5 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\) and \(202,100 \mathrm{~J} / \mathrm{mol}\), respectively.

Aluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of \(\mathrm{Al}\) in this silicon material is known to be \(3 \times 10^{19}\) atoms/m \(^{3}\). The drive-in diffusion treatment is to be carried out at \(1050^{\circ} \mathrm{C}\) for a period of \(4.0 \mathrm{~h}\), which gives a junction depth \(x_{j}\) of \(3.0 \mu \mathrm{m}\). Compute the predeposition diffusion time at \(950^{\circ} \mathrm{C}\) if the surface concentration is maintained at a constant level of \(2 \times 10^{25}\) atoms \(/ \mathrm{m}^{3}\). For the diffusion of \(\mathrm{Al}\) in \(\mathrm{Si}\), values of \(Q_{d}\) and \(D_{0}\) are \(3.41\). \(\mathrm{eV} /\) atom and \(1.38 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\), respectively.

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