Calculator Inputs
Formula Used
Sodium chloride has a rock salt structure. It can be treated as a face-centered chloride lattice with sodium shifted by half a cell edge. The general structure factor is:
F(hkl) = Σ fj exp[2πi(hxj + kyj + lzj)]
For ideal sodium chloride:
F = 0 when h, k, and l are mixed odd and even.
F = 4(fCl + fNa) when h, k, and l are all even.
F = 4(fCl - fNa) when h, k, and l are all odd.
Thermal motion is included as f corrected = f exp[-B(sin θ / λ)²]. Relative intensity is estimated as I = scale × multiplicity × Lorentz factor × |F|².
How to Use This Calculator
Enter the Miller indices h, k, and l for the reflection. Add sodium and chloride scattering factors from your table or diffraction source. Keep anomalous correction fields at zero when they are not required. Add B factors and sin θ / λ when thermal correction is needed. Press the calculate button. The result appears above the form and below the header section. Use the CSV or PDF button to save the result.
Example Data Table
| h | k | l | Rule | Formula | Expected Trend |
|---|---|---|---|---|---|
| 1 | 0 | 0 | Mixed | F = 0 | Forbidden |
| 1 | 1 | 1 | All odd | F = 4(fCl - fNa) | Allowed, weaker |
| 2 | 0 | 0 | All even | F = 4(fCl + fNa) | Allowed, stronger |
| 2 | 2 | 0 | All even | F = 4(fCl + fNa) | Allowed, strong |
Article: Structural Factor of Sodium Chloride
Crystal Meaning
The structure factor links atomic arrangement with diffraction strength. In sodium chloride, this value is especially useful because the crystal has a simple and important rock salt pattern. Chloride ions form a face centered cubic arrangement. Sodium ions occupy shifted positions inside the same repeating cell.
Reflection Rules
The Miller indices control whether a reflection is visible. If h, k, and l are mixed odd and even, the face centered part cancels the wave. The reflection becomes systematically absent. This is called an extinction rule. It is a key test for cubic symmetry.
Even and Odd Cases
When h, k, and l are all even, sodium and chloride waves add together. The formula becomes four times the sum of both scattering factors. These peaks are usually strong. When all three indices are odd, the sodium wave subtracts from the chloride wave. The peak remains allowed, but it may be weaker.
Scattering Strength
Atomic scattering factors are not fixed constants in detailed work. They depend on scattering angle and radiation type. Chloride often scatters more strongly than sodium because it has more electrons. This difference helps create intensity contrast between odd and even reflections.
Thermal Correction
Real crystals are not perfectly still. Ions vibrate about their average positions. The B factor reduces scattering as angle increases. This calculator includes that option through the Debye expression. It lets users compare ideal and corrected values in one form.
Intensity Estimate
The measured peak intensity is related to the square of the structure factor magnitude. Multiplicity, scale, and Lorentz correction can also change the final value. The calculator therefore reports amplitude, phase, spacing, scattering vector, and relative intensity.
Practical Use
Students can use the tool to learn extinction rules. Laboratory users can test expected NaCl reflections before indexing a pattern. The result is not a full refinement program. It is a focused calculator for fast checks, teaching, and report preparation.
FAQs
What is the structure factor?
The structure factor is a complex value that describes how atoms in a crystal scatter X-rays for a chosen reflection.
Why is sodium chloride useful for this calculation?
Sodium chloride has a clear rock salt structure. Its reflection rules show face centered extinction and basis interference in a simple way.
When is a sodium chloride reflection forbidden?
A reflection is forbidden when h, k, and l are mixed odd and even. The face centered lattice contribution cancels out.
What happens when all indices are even?
All even reflections are allowed. Sodium and chloride contributions add, so the simplified formula is F = 4(fCl + fNa).
What happens when all indices are odd?
All odd reflections are allowed. Sodium subtracts from chloride, so the simplified formula is F = 4(fCl - fNa).
Why does the calculator include B factors?
B factors estimate the effect of thermal vibration. Larger values reduce the effective scattering factor, especially at higher scattering angle.
Is the intensity result absolute?
No. It is a relative estimate based on scale, multiplicity, Lorentz factor, and squared structure factor magnitude.
Can I use anomalous corrections?
Yes. Enter f prime and f double prime values when your radiation source or analysis requires anomalous scattering terms.