1. calculation of F²: the 200-reflection

   
   d _hkl = a/(h² + k² + l²)^1/2
   For hkl = 200 this is:
   d ₂₀₀ = 5.638/(2² + 0² + 0²)^1/2 = 5.638/ 4 = 2.819 Å
   Bragg's law
   sin q/l = 0.1774 Å^-1

   atomic scattering factor f_n: after interpolation

   sin q/l	0.15	0.1774	0.20
   fNa+	9.035	8.6815	8.39
   fCl-	14.12	13.0678	12.20

   cosine part of F₂₀₀
   

   8.6815 cos {2p (2.0 + 0.0 + 0.0)}
   + 8.6815 cos {2p (2.0 + 0.1/2 + 0.1/2)}
   + 8.6815 cos {2p (2.1/2 + 0.0 + 0.1/2)}
   + 8.6815 cos {2p (2.1/2 + 0.1/2 + 0.0)}
   + 13.0678 cos {2p (2.1/2 + 0.0 + 0.0)}
   + 13.0678 cos {2p (2.0 + 0.1/2 + 0.0)}
   + 13.0678 cos {2p (2.0 + 0.0 + 0.1/2)}
   + 13.0678 cos {2p (2.1/2 + 0.1/2 + 0.1/2)}
   = 8.6815 (cos 0 + cos 0 + cos 2p + cos 2p)
   + 13.0678 (cos 2p + cos 0 + cos 0 + cos 2p)
   = 86.9972

   sine part of F₂₀₀
   

   8.6815 sin {2p (2.0 + 0.0 + 0.0)}
   + 8.6815 sin {2p (2.0 + 0.1/2 + 0.1/2)}
   + 8.6815 sin {2p (2.1/2 + 0.0 + 0.1/2)}
   + 8.6815 sin {2p (2.1/2 + 0.1/2 + 0.0)}
   + 13.0678 sin {2p (2.1/2 + 0.0 + 0.0)}
   + 13.0678 sin {2p (2.0 + 0.1/2 + 0.0)}
   + 13.0678 sin {2p (2.0 + 0.0 + 0.1/2)}
   + 13.0678 sin {2p (2.1/2 + 0.1/2 + 0.1/2)}
   = 8.6815 (sin 0 + sin 0 + sin 2p + sin 2p)
   + 13.0678 (sin 2p + sin 0 + sin 0 + sin 2p)
   = 0

   combining both parts: F₂₀₀² = 86.9972² + 0² = 7568 = I ₂₀₀

2. calculation of F²: the 100-reflection

   
   d _hkl = a/(h² + k² + l²)^1/2
   For hkl = 100 this is:
   d ₁₀₀ = 5.638/(1² + 0² + 0²)^1/2 = 5.638/ 1 = 5.638 Å
   Bragg's law
   sin q/l = 0.08868 Å^-1

   cosine part of F₁₀₀
   

   f_Na⁺ cos {2p (1.0 + 0.0 + 0.0)}
   + f_Na⁺ cos {2p (1.0 + 0.1/2 + 0.1/2)}
   + f_Na⁺ cos {2p (1.1/2 + 0.0 + 0.1/2)}
   + f_Na⁺ cos {2p (1.1/2 + 0.1/2 + 0.0)}
   + f_Cl^- cos {2p (1.1/2 + 0.0 + 0.0)}
   + f_Cl^- cos {2p (1.0 + 0.1/2 + 0.0)}
   + f_Cl^- cos {2p (1.0 + 0.0 + 0.1/2)}
   + f_Cl^- cos {2p (1.1/2 + 0.1/2 + 0.1/2)}
   = f_Na⁺ (cos 0 + cos 0 + cos p + cos p)
   + f_Cl^- (cos p + cos 0 + cos 0 + cos p)
   = 0

   sine part of F₁₀₀
   

   f_Na⁺ sin {2p (1.0 + 0.0 + 0.0)}
   + f_Na⁺ sin {2p (1.0 + 0.1/2 + 0.1/2)}
   + f_Na⁺ sin {2p (1.1/2 + 0.0 + 0.1/2)}
   + f_Na⁺ sin {2p (1.1/2 + 0.1/2 + 0.0)}
   + f_Cl^- sin {2p (1.1/2 + 0.0 + 0.0)}
   + f_Cl^- sin {2p (1.0 + 0.1/2 + 0.0)}
   + f_Cl^- sin {2p (1.0 + 0.0 + 0.1/2)}
   + f_Cl^- sin {2p (1.1/2 + 0.1/2 + 0.1/2)}
   = f_Na⁺ (sin 0 + sin 0 + sin p + sin p)
   + f_Cl^- (sin p + sin 0 + sin 0 + sin p)
   = 0

   combining both parts: F₁₀₀² = 0² + 0² = 0 = I ₁₀₀

   Diffraction will only occur when the Laue conditions are fullfilled.
   This requires that simultaneous S.a = h; S.b = k; S.c = l.

j₂₀₀ = 6
i.e. 2,0,0; 0,2,0 ; 0,0,2; -2,0,0; 0,-2,0; 0,0,-2

Using Bragg's law: 1.54 = 2 x 2.819 x sin q
0.273 = sin q
2q = 31,69°

P₂₀₀ = (1 + cos²2q)/2
P₂₀₀ = 0.862

L = 1/(sin²q cosq)
L = 13.95

Results:

1. Due to the powder: was there preferred orientation leading to different peak intensities? Was the particle size small enough so that all possible orientations were statisticaly present? How was the sample prepared (grounded and sieved)? Was the sample spinned during the experiment? How pure was the product and did it remain stable during the XRD-experiment (hydratation?), ...
2. Other indicent X-rays used (for example Mo instead of Cu): this leads to other factors in the equatation, other indicent wavelenght,...
   Other experimental set-up: for example grazing incidence, using filter or monochromator,other detector (and perhaps bad calibrated - for a PSD-detector)...
3. Bad alignment of the diffractometer (not focussed), detector slightly miss positioned, ...
4. Was the background ignored or not? (If the background varies with the angle, this leads to different intensities)
5. Broadening and shift of peaks due to sample transparency?
6. What was the step-size used in the experiment? (Perhaps too large: bad resolution.) If the step time varies with 2q, the intensity will be different.