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We report improved precision measurements of the Van der Waals potentialstrength ($C_3$) for Na atoms and a silicon-nitride (SiN$_x$) surface. Westudied diffraction from nano-fabricated gratings with a particular "magic"open-fraction that allows us to determine $C_3$ without the need for separatemeasurements of the width of the grating openings. Therefore, finding the magicopen-fraction improves the precision of $C_3$ measurements. The same effect isdemonstrated for a grating with an arbitrary open-fraction by rotating it to aparticular "magic" angle, yielding $C_3=3.42\pm 0.19 \textrm{eV}\mathring{\textrm{A}}^3$ for Na and a SiN$_x$ surface. This precision issufficient to detect a change in $C_3$ due to a thin metal coating on thegrating surface. We discuss the contribution to $C_3$ of core electrons andedge effects.

Magic ratio of window width to grating period for Van der Waals potential measurements using material gratings