Question about a cubic crystal and its parameters

Click For Summary

Homework Help Overview

The discussion revolves around a problem related to cubic crystal structures, specifically focusing on the parameters and calculations involving the radius of ions in a CsCl structure. Participants are examining the relationships between geometric dimensions and ionic radii.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss methods for calculating the radius of ion A by utilizing the diagonal of a square and the geometry of the cubic structure. There are questions about the number of nearest neighbors and the implications of different crystal structures.

Discussion Status

Some participants have provided insights and hints regarding the calculations and assumptions about the crystal structure. There is an ongoing exploration of the correct parameters and relationships, with no explicit consensus reached yet.

Contextual Notes

There are indications of confusion regarding the correct values for the radius and the assumptions about the crystal structure, particularly in relation to the CsCl model. The original poster's calculations differ from expected results, prompting further discussion.

Clara Chung
Messages
300
Reaction score
13

Homework Statement


27.png


Homework Equations

The Attempt at a Solution


28.png

So i got the answer by finding the diagonal of the square and then find the radius of A.
([(2x0.17)2 ]x2 )1/2 = 2a + 2x0.17
And find out a= 0.14 nm , however the answer is 0.124nm, please help
 

Attachments

  • 27.png
    27.png
    9.4 KB · Views: 810
  • 28.png
    28.png
    4.2 KB · Views: 805
Physics news on Phys.org
I think this is a 3D problem.
 
  • Like
Likes   Reactions: Clara Chung and Lord Jestocost
Clara Chung said:

Homework Statement


View attachment 224603

Homework Equations

The Attempt at a Solution


View attachment 224604
So i got the answer by finding the diagonal of the square and then find the radius of A.
([(2x0.17)2 ]x2 )1/2 = 2a + 2x0.17
And find out a= 0.14 nm , however the answer is 0.124nm, please help
The number of nearest neighbors are 8, it is CsCl structure:

upload_2018-4-24_18-4-14.png

In your drawing, the number of nearest neighbors are 6.
 

Attachments

  • upload_2018-4-24_18-4-14.png
    upload_2018-4-24_18-4-14.png
    9.7 KB · Views: 333
  • Like
Likes   Reactions: Clara Chung
Clara Chung said:

Homework Statement


View attachment 224603

Homework Equations

The Attempt at a Solution


View attachment 224604
So i got the answer by finding the diagonal of the square and then find the radius of A.
([(2x0.17)2 ]x2 )1/2 = 2a + 2x0.17
And find out a= 0.14 nm , however the answer is 0.124nm, please help
Yes, the crystal structure can be simply identified identical to the CsCl where Cl- forms a cubic lattice and Cs+ occupies the body centers(cubic voids). Now you can easily use the radius ratio(r+/r-) for cubic void(here for smallest value of A use lower limit of the radius ratio range) to find out the radius of A
hint: here it is assumed that B forms the lattice and A occupies the voids
Hope that helps... [emoji4]
images%20(1).jpeg
 

Attachments

  • images%20(1).jpeg
    images%20(1).jpeg
    21.4 KB · Views: 335
  • Like
Likes   Reactions: Clara Chung
Thanks everyone for the pictures and information. I got the answer by using the diagonal of the cube. [[3x(2x0.17)2]1/2 - 2x(0.17)]/2 = 0.124
 

Similar threads

Minimum Energy for Bragg Reflection in Cubic Crystals
  • · Replies 1 ·
Replies
1
Views
1K
Finding nearest neighbour equilibrium distance
  • · Replies 4 ·
Replies
4
Views
3K
Energy of a crystal in thermal equilibrium
  • · Replies 1 ·
Replies
1
Views
3K
Number of modes in Cubic Cavity
  • · Replies 2 ·
Replies
2
Views
3K
Electric Flux through Cubical Surface Enclosing Sphere
  • · Replies 2 ·
Replies
2
Views
4K
[PoM] Electrons Fermi level in a crystal
  • · Replies 8 ·
Replies
8
Views
2K
Crystallography, diffraction, identifying the pure element
  • · Replies 1 ·
Replies
1
Views
2K
Potential Energy of a 2D Crystal Lattice
  • · Replies 6 ·
Replies
6
Views
3K
Miller Indices (Solid State Physics)
  • · Replies 1 ·
Replies
1
Views
3K
Crystal frames problem, what actually asking?
  • · Replies 2 ·
Replies
2
Views
1K