# Calculation of Intensity of of AX crystals

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1. Mar 3, 2015

### ralden

I'm still confuse on using the equation about atomic scattering factor, f = a*e^(-b+((sin(theta)/lamda)^2) + c (general equation),

where sin(theta)/lamda = 1/2d = 1/(2*(sqrt(a^2/(h^2 + k^2 +l^2)))), so this term is dependent on the plane.
which you will used to find the Intensity of crystals in a certain plane. I = F^2 (disregard multiplicity factor, absorption and etc.), F = f*cos(2pi(hx + ky + lz)) (i omitted the isine part)

so given a compound NaCl where a, b and c are also given, i try to so solve I in 111 plane.

first i solve fNa and fCl using the equation above, this gives 26.30, and 23.71 respectively, and substitute to the equation of intensity i got I(NaCl)=106.44, but when i'm try to check using related literature, some website (http://pd.chem.ucl.ac.uk/pdnn/diff2/structf.htm) and its jcpds, my answer was wrong so please enlighten me about this matter.

constant i used:
for Na:
a1Na=3.2565;b1Na=2.6671;a2Na=23.9362;b2Na=6.1153;a3Na=1.3998;b3Na=0.2001;a4Na=1.0032;b4Na=14.039;c1Na=0.404;
for Cl:
a1Cl=18.2915;b1Cl=0.0066; a2Cl=17.604; b2Cl=1.1717;a3Cl=6.5337;b3Cl=19.5424;a4Cl=2.3386;b4Cl=60.4486;c1Cl=-16.378;

2. Mar 3, 2015

### M Quack

The formula for the atomic (or ionic) scattering factor given here

http://scripts.iucr.org/cgi-bin/paper?sh0059

is

$f(s) = \sum\limits_{i=1}^{4}a_i \exp(-b_i s^2) +c \\ s = \sin(\theta)/\lambda = Q/4\pi = 1/2d$

(you have a "+" which is probably a typo)

You should use the scattering factors for the ions, Na+ and Cl-

The constants given in the paper look a bit different from yours, but I have not checked every one of them.

3. Mar 3, 2015

### ralden

Last edited: Mar 3, 2015