  Ti-Ta-X (X = Al, Sn, Zr) compounds are emerging candidates as
high-temperature shape memory alloys (HTSMAs). The stability of the one-way
shape memory effect (1WE), the exploitable pseudoelastic (PE) strain intervals
as well as the transformation temperature in these alloys depend strongly on
composition, resulting in a trade-off between a stable shape memory effect and
a high transformation temperature. In this work, experimental measurements and
first-principles calculations are combined to rationalize the effect of
alloying a third component to Ti-Ta based HTSMAs. Most notably, an
$\textit{increase}$ in the transformation temperature with increasing Al
content is detected experimentally in Ti-Ta-Al for low Ta concentrations, in
contrast to the generally observed dependence of the transformation temperature
on composition in Ti-Ta-X. This inversion of trend is confirmed by the
$\textit{ab-initio}$ calculations. Furthermore, a simple analytical model based
on the $\textit{ab-initio}$ data is derived. The model can not only explain the
unusual composition dependence of the transformation temperature in Ti-Ta-Al,
but also provide a fast and elegant tool for a qualitative evaluation of other
ternary systems. This is exemplified by predicting the trend of the
transformation temperature of Ti-Ta-Sn and Ti-Ta-Zr alloys, yielding a
remarkable agreement with available experimental data.
