Question about a cubic crystal and its parameters

[Clara Chung]

Homework Statement

Homework Equations

The Attempt at a Solution

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

 

[Dr Dr news]

I think this is a 3D problem.

 

[ehild]

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:

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

 

[jishnu]

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]

 

[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