Distance to 3rd and 5th nearest ion to S2- in ZnS structure

In summary, the conversation discusses the structure of ZnS and the distance to the 3rd and 5th nearest ions in relation to the unit cell's edge length. The table attached shows the number of nearest neighbors and their distances for an S2- ion. The speaker is seeking help in proving the equation for the distance to the 3rd and 5th nearest ions.
  • #1
Vishesh Jain
9
0
Please post this type of questions in the HW section using the template and showing your work.
Hey folks

ZnS has a ccp structure with S2- ions forming FCC lattice with Zn2+ ions at half the tetrahedral voids

zbcell.gif


Attached is a table showing no. of nearest neighbours and their distance for an S2- ion

'a' is edge length of the unit cell

I want to know how the distance to the 3rd & 5th nearest ion is √11a/4 & √19a/11, i.e how to prove this.
upload_2018-10-13_16-17-34.png
Thanks ... any help is appreciated
 

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  • #2
Have you you tried to follow the geometry? Often it is enough to find right right triangles and use Pythagorean theorem.
 
  • #3
I think those numbers are wrong. They're not what I get (with quick mental arithmetic).
 
  • #4
yes i did pythogarus & got it ... thanks ...
 

1. What is the distance between the S2- ion and the 3rd nearest ion in the ZnS structure?

The distance between the S2- ion and the 3rd nearest ion in the ZnS structure will vary depending on the specific structure and arrangement of atoms in the crystal lattice. However, on average, this distance is typically around 3 to 4 angstroms.

2. How does the distance to the nearest ions affect the properties of ZnS?

The distance to the nearest ions in the ZnS structure can have a significant impact on its properties. This distance affects the strength of the bonds between the atoms, which in turn affects the hardness, melting point, and other physical and chemical properties of the material.

3. How is the distance to the 5th nearest ion calculated in the ZnS structure?

The distance to the 5th nearest ion is calculated by measuring the distance between the central S2- ion and the 5th closest ion in the crystal lattice. This can be done using various experimental techniques, such as X-ray diffraction or electron microscopy.

4. Can the distance to the 3rd and 5th nearest ions be manipulated in the ZnS structure?

Yes, the distance to the 3rd and 5th nearest ions can be manipulated by altering the conditions during the formation of the ZnS crystal. For example, changing the temperature, pressure, or concentration of atoms during crystallization can affect the distance between ions in the structure.

5. How does the distance to the nearest ions impact the electronic properties of ZnS?

The distance to the nearest ions can affect the electronic properties of ZnS by influencing the energy levels and band structure of the material. A shorter distance between ions can lead to a larger band gap, making the material more insulating, while a longer distance can decrease the band gap and make the material more conductive.

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