Calculating Dislocation Chain Length in Solids

[mate1000]

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.

 

[faen]

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.

 

[denian]

I would approach this question by first understanding the concept of dislocation chain length in solids. Dislocations refer to defects in the atomic structure of a solid material, where the atoms are not arranged in their perfect lattice positions. These dislocations can act as barriers to the movement of atoms and can affect the mechanical properties of the material. The dislocation density is a measure of the number of dislocations per unit volume of material.

To calculate the dislocation chain length in a solid, we need to consider the dislocation density and the volume of the material. In this case, we are given the dislocation density of 10^4 mm^-2 and the volume of 1 cm^3. We can use these values to calculate the length of the dislocation chain by dividing the volume by the dislocation density.

1 cm^3 is equal to 10^-6 m^3 and 10^4 mm^-2 is equal to 10^8 m^-2. Therefore, the length of the dislocation chain would be 10^-14 m or 0.00001 micrometers.

Now, let's consider the second scenario where the dislocation density is increased to 10^10 mm^-2 by cold working. Following the same calculation method, we can determine that the length of the dislocation chain in 1 cm^3 of material would be 10^-20 m or 0.00000000001 micrometers. This is significantly smaller than the previous length, indicating that the higher dislocation density results in a shorter dislocation chain.

Overall, this exercise highlights the incredibly small scale at which dislocations operate in solid materials. The dislocation chain length in a 1 cm^3 volume of material is only a few micrometers, even with a high dislocation density. This demonstrates the importance of understanding and controlling dislocations in materials, as they can have a significant impact on the properties and performance of the material.