Mean free path and collisional cross section in Na due to impurities

[petr1243]

Let's say that we have Na at room temperature. The concentration of Na becomes plus one percent due to impurities. I'm interested in finding the mean free path and collisional cross section due to these impurities. I'm not sure on how Matheissen's rule could be applied, if we don't know what the lattice mean free path and time are. Kittel does a horrible job in explaining this concept, and Ziman's text will probably get me scratching my head for the whole semester. Could some one also discuss some possibilities for the occurences of these impurities. Any suggestions would be much appreciated.

 

[BigJDubs]

Matheissen's rule is a general rule used to calculate the mean free path (MFP) and collisional cross section (CCS) of a given material based on its lattice structure. The MFP is the average distance a particle can travel before it collides with another particle or obstacle. The CCS is the area over which a particle interacts with other particles or obstacles when it collides.Matheissen's rule is derived from the Boltzmann equation, and states that the MFP is proportional to the square of the lattice constant (a2), divided by the number of atoms per unit volume (N) times the CCS:MFP = a2/N*CCSIn order to use Matheissen's rule for calculating the MFP and CCS of Na at room temperature due to impurities, you would need to know the lattice constant of Na, the number of atoms per unit volume, and the CCS. Unfortunately, without knowing these values, it is impossible to use Matheissen's rule to accurately calculate the MFP and CCS.The lattice constant and number of atoms per unit volume of Na can easily be found in literature, but the CCS is more difficult to determine. It will depend on the type of impurities present as well as the concentration of those impurities. Generally speaking, the higher the concentration of impurities, the higher the CCS will be. In order to determine the CCS of Na due to impurities at room temperature, you would need to perform detailed experiments and measurements. It is also worth noting that if the impurities are in the form of ions, then the MFP and CCS could be determined using the Debye-Huckel theory. This theory uses the ionic strength of the solution to calculate the MFP and CCS.

 

[charng]

I would like to clarify and provide some insights on the concepts of mean free path and collisional cross section in the context of impurities in Na at room temperature.

Mean free path is defined as the average distance a particle travels before undergoing a collision. In this case, the impurities in Na act as scattering centers, causing the Na particles to deviate from their original trajectory and undergo collisions. The concentration of impurities plays a crucial role in determining the mean free path, as a higher concentration would lead to more frequent collisions and thus a shorter mean free path.

Collisional cross section, on the other hand, is a measure of the effective area presented by a particle for collisions to occur. In the case of impurities in Na, the impurities themselves act as the scattering centers and their size and shape determine the collisional cross section. A higher concentration of impurities would also lead to a larger collisional cross section.

Now, in order to calculate the mean free path and collisional cross section in Na due to impurities, knowledge of the lattice mean free path and time is required. However, in this scenario, it is not necessary to know these values as we are only interested in the effects of impurities on the mean free path and collisional cross section.

As for the occurrence of these impurities, there are several possibilities. They could be introduced during the manufacturing process of Na, or they could be present in the environment where Na is stored or used. The source of impurities could also be from the materials used in the containers or equipment used to handle Na.

In conclusion, mean free path and collisional cross section are important concepts to consider when studying the effects of impurities on the behavior of Na particles. Further research and experimentation would be needed to accurately determine these values in the given scenario. Additionally, thorough understanding of the properties and sources of impurities is crucial in order to minimize their impact on the behavior of Na.