ConceptCheck5

# ConceptCheck5 - increases with increasing temperature...

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120 Concept Check 5.1 Question: Rank the magnitudes of the diffusion coefficients from greatest to least for the following systems: N in Fe at 700 ° C Cr in Fe at 700 ° C N in Fe at 900 ° C Cr in Fe at 900 ° C Now justify this ranking. ( Note: Both Fe and Cr have the BCC crystal structure, and the atomic radii for Fe, Cr, and N are 0.124, 0.125, and 0.065 nm, respectively. You may also want to refer to Section 4.3 .) Answer: The diffusion coefficient magnitude ranking is as follows: N in Fe at 900 ° C; D N (900) N in Fe at 700 ° C; D N (700) Cr in Fe at 900 ° C; D Cr (900) Cr in Fe at 700 ° C; D Cr (700) Nitrogen is an interstitial impurity in Fe (on the basis of its atomic radius), whereas Cr is a substitutional impurity. Since interstitial diffusion occurs more rapidly than substitutional impurity diffusion, D N > D Cr . Also, inasmuch as the magnitude of the diffusion coefficient

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Unformatted text preview: increases with increasing temperature, D (900) > D (700). Concept Check 5.2 Question: Consider the self-diffusion of two hypothetical metals A and B. On a schematic graph of ln D versus 1/T, plot (and label) lines for both metals given that D (A) > D (B) and also that Q d (A) > Q d (B). Answer: The schematic ln D versus 1/ T plot with lines for metals A and B is shown below. As explained in the previous section, the intercept with the vertical axis is equal to ln D . As shown in this plot, the intercept for metal A is greater than for metal B inasmuch as D (A) > D (B) [alternatively ln D (A) > ln D (B)]. In addition, the slope of the line is equal to – Q d /R . The two lines in the plot have been constructed such that negative slope for metal A is greater than for metal B, inasmuch as Q d (A) > Q d (B)...
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