After calculation, I found F440 = 8fa+16fb+32fo

Dear Sir 

Thank you for the ans. Yes, I was also expecting 16fb instead of 32fb. But, i am unable to rectify it. So, may i request you to please give the calculation details for 16fb.

In fact, the calculation in the docx file you sent me are correct. If you are familiar with the python langage, see below the detail of the script i have used to check your calculation (I just copy/past the different expressions you wrote on the file for each complex numbers) :

"""

import numpy as np

cos=np.cos

sin=np.sin

pi=np.pi

u=0.375

a0=complex(cos(2*pi*(4*0+4*0+0*0)),sin(2*pi*(4*0+4*0+0*0)))

a1=complex(cos(2*pi*(4*(1/4)+4*(1/4)+0*(1/4))),sin(2*pi*(4*(1/4)+4*(1/4)+0*(1/4))))

b0=complex(cos(2*pi*(4*(5/8)+4*(5/8)+0*(5/8))),sin(2*pi*(4*(5/8)+4*(5/8)+0*(5/8))))

b1=complex(cos(2*pi*(4*(5/8)+4*(7/8)+0*(7/8))),sin(2*pi*(4*(5/8)+4*(7/8)+0*(7/8))))

b2=complex(cos(2*pi*(4*(7/8)+4*(5/8)+0*(7/8))),sin(2*pi*(4*(7/8)+4*(5/8)+0*(7/8))))

b3=complex(cos(2*pi*(4*(7/8)+4*(7/8)+0*(5/8))),sin(2*pi*(4*(7/8)+4*(7/8)+0*(5/8))))

c0=complex(cos(2*pi*(4*u+4*u+0*u)),sin(2*pi*(4*u+4*u+0*u)))

c1=complex(cos(2*pi*(4*(1/4 - u)+4*(1/4 - u)+0*(1/4 - u))),sin(2*pi*(4*(1/4 - u)+4*(1/4 - u)+0*(1/4 - u))))

c2=complex(cos(2*pi*(4*u+4*(-u)+0*(-u))),sin(2*pi*(4*u+4*(-u)+0*(-u))))

c3=complex(cos(2*pi*(4*(1/4 - u)+4*(1/4 + u)+0*(1/4 + u))),sin(2*pi*(4*(1/4 - u)+4*(1/4 + u)+0*(1/4 + u))) )

c4=complex(cos(2*pi*(4*(-u)+4*u+0*(-u))),sin(2*pi*(4*(-u)+4*u+0*(-u))))

c5=complex(cos(2*pi*(4*(1/4 + u)+4*(1/4 - u)+0*(1/4 + u))),sin(2*pi*(4*(1/4 + u)+4*(1/4 - u)+0*(1/4 + u))))

c6=complex(cos(2*pi*(4*(-u)+4*(-u)+0*u)),sin(2*pi*(4*(-u)+4*(-u)+0*u)))

c7=complex(cos(2*pi*(4*(1/4 + u)+4*(1/4 + u)+0*(1/4 - u))),sin(2*pi*(4*(1/4 + u)+4*(1/4 + u)+0*(1/4 - u))))

factor_1=[a0,a1]

factor_2=[b0,b1,b2,b3]

factor_3=[c0,c1,c2,c3,c4,c5,c6,c7]

print 4*np.sum(factor_1)

print 4*np.sum(factor_2)

print 4*np.sum(factor_3)

"""

by launching the script, i obtain the following result:

"

(8+0j)

(16+0j)

(32+0j)

"

It's the expected result, therefore, it means that your starting eqyuation is correct

best wishes,

Thank you sir for the confirmation. Unfortunately i am not familiar with python, actually it was matlab code and i have got 32fb. 

Sir, I have missed something (a multiplication factor of 2 in fb term) in the formula I sent to you. The correct one should be like this form:

(complex term)*fa + (complex term)*2*fb +  (complex term)*fo 

for normal spinel (A) [B2] O4

for the complex term for fb i have got 16 + 0i (if 2 is neglected)

I confirm that the structure factor for the plane (440) as quoted by Christopher i. e. 

F440 = 8 (FA+ 2 FB+ 4 FO).

I do not mind to check your calculations. If you like try to send me your excel sheet.

Thank yo

Okay sir, I will send it

thanks

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