  Coating detector materials with films highly reflective in the ultraviolet
region improves sensitivity of the rare-event detectors that use liquid xenon.
In this work, we investigate the MgF$_2$-Al-MgF$_2$ coating designed to achieve
high reflectance at 175 nm, the mean wavelength of liquid xenon (LXe)
scintillation. The coating was applied to an unpolished, passivated copper
substrate mimicking a realistic detector component of the proposed nEXO
experiment, as well as to two unpassivated substrates with "high" and "average"
levels of polishing. After confirming the composition and morphology of the
thin-film coating using TEM and EDS, the samples underwent reflectance
measurements in LXe and gaseous nitrogen (GN2). Measurements in LXe exposed the
coated samples to -100 $\deg$C for several hours. No peeling of the coatings
was observed after several thermal cycles. Polishing is found to strongly
correlate with the measured specular reflectance ($R_{\mathrm{spec}}$). In
particular, 5.8(5)% specular spike reflectance in LXe was measured for the
realistic sample at 20$\deg$ of incidence, while the values for similar angles
of incidence on the high and average polish samples are 62.3(1.3)% and
27.4(7)%, respectively. At large angles (66\deg--75$\deg$), the
$R_{\mathrm{spec}}$ in LXe for the three samples increases to 23(5)%, 80(8)%,
and 84(18)%, respectively. The $R_{\mathrm{spec}}$ at around 45$\deg$ was
measured in both GN2 and LXe for average polish sample and shows a reasonable
agreement. Importantly, the total reflectance of the samples is comparable and
estimated to be 92(8)%, 85(8)%, and 83(8)% in GN2 for the realistic, average,
and high polish samples, respectively. This is considered satisfactory for the
next-generation LXe experiments that could benefit from using reflective films,
such as nEXO and DARWIN, thus validating the design of the coating.
