Question about a cubic crystal and its parameters

  • #1
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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
 

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Answers and Replies

  • #2
122
35
I think this is a 3D problem.
 
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  • #3
ehild
Homework Helper
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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.
 

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  • #4
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15

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
 

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  • #5
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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
 

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