= Solution
The $(111)$ reflection is allowed, with $d_{111}=0.3233\,\mathrm{nm}$ and \b[$2\theta_B=27.56^\circ$]. Its odd-parity amplitude is proportional to $f_{\rm Cl}-f_{\rm Na}$, generally weaker than the corresponding sum. Its normal makes $\cos^{-1}(1/\sqrt3)=54.74^\circ$ with the $[100]$ surface normal.
It is therefore \b[not obtained in the ordinary symmetric scan of that face], despite its modest <Bragg angle>. In a usual edge-aligned cubic mounting its normal also has an out-of-horizontal-plane component. A suitable multi-axis reorientation, or a crystal cut with a $(111)$ face, makes the reflection accessible; a thin specimen in transmission or a powder experiment is another route. Tilting the scattering vector does not by itself ensure front-face reflection: because $54.74^\circ$ exceeds $\theta_B=13.78^\circ$, incident and outgoing rays for that highly asymmetric orientation cannot both lie outside the same flat $(100)$ face. A suitable specimen shape/transmission path or recut face is needed.
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