  We present thermal expansion and longitudinal magnetostriction data for cubic
RAl3 (R = Tm, Yb, Lu) single crystals. The thermal expansion coefficient for
YbAl3 is consistent with an intermediate valence of the Yb ion, whereas the
data for TmAl3 show crystal electric field contributions and have strong
magnetic field dependencies. de Haas-van Alphen-like oscillations were observed
in the magnetostriction data of YbAl3 and LuAl3, several new extreme orbits
were measured and their effective masses were estimated. Zero and 140 kOe
specific heat data taken on both LuAl3 and TmAl3 for T < 200 K allow for the
determination of a CEF splitting scheme for TmAl3.
