Calculating Dislocation Chain Length in Solids

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SUMMARY

The discussion focuses on calculating the dislocation chain length in solids, specifically in metals with varying dislocation densities. For a dislocation density of 104 mm-2, the total chain length of dislocations in 1 cm3 is approximately 100 km. When the dislocation density increases to 1010 mm-2 due to cold working, the chain length extends significantly, necessitating precise calculations based on average dislocation lengths. Participants emphasize the importance of understanding dislocation density and its impact on material properties.

PREREQUISITES
  • Understanding of dislocation density in materials science
  • Familiarity with atomic defects in solids
  • Basic knowledge of volume calculations in cubic centimeters
  • Concept of cold working and its effects on metals
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  • Research methods for calculating dislocation density in metals
  • Learn about the effects of cold working on dislocation structures
  • Explore techniques for measuring average dislocation lengths
  • Investigate the relationship between dislocation density and mechanical properties of materials
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Materials scientists, metallurgists, and engineers involved in the study of metal properties and the effects of dislocations on material performance.

mate1000
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To provide some perspective on the dimensions of atomic defects in solids, consider a metal specimen that has a dislocation density of 10^4 mm^-2. Suppose that all the dislocations in 1 cm^3 were somehow removed and linked end-to-end. How far (in km) would the chain extend? Now suppose that the density is increased to 10^10mm^-2 by cold working. What would the chain length of dislocations in 1 cm^3 of material?

Can anyone help me with this question, it has me stumped.
 
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Perhaps if you can determine the average dislocation length in a metal you can multiply it with the dislocation density, or if they are longer than a cm multiply the dislocation density with 1 cm.
 

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