  Finite-temperature ductility-brittleness and electronic structures of
Al$_3$Sc, Al$_2$Sc and AlSc are studied comparatively by first-principles
calculations and ab-initio molecular dynamics. Results show that Al$_3$Sc and
Al$_2$Sc are inherently brittle at both ground state and finite temperatures.
By contrast, AlSc possesses a significantly superior ductility evaluated from
all Pugh's, Pettifor's and Poisson's ductility-brittleness criteria. At ground
state, AlSc meets the criteria of ductile according to Pugh's and Poisson's
theories, while it is categorized as the brittle in the frame of Pettifor's
picture. With the increasing temperature, the ductility of all the studied
compounds exhibits a noticeable improvement. In particular, as the temperature
rises, the Cauchy pressure of AlSc undergoes a transition from negative to
positive. Thus, at high temperatures (T > 600 K), AlSc is unequivocally
classified as the ductile from all criteria considered. In all Al$_3$Sc,
Al$_2$Sc and AlSc, the Al-Al bond, originated from s-p and p-p orbital
hybridizations, and the Al-Sc bond, dominated by p-d covalent hybridization,
are the first and second strongest chemical bonds, respectively. To explain the
difference in mechanical properties of the studied compounds, the mean bond
strength (MBS) is evaluated. The weaker Al-Al bond in AlSc, leading to a
smaller MBS, could be the origin for the softer elastic stiffness and superior
intrinsic ductility. The longer length of the Al-Al bond in AlSc is responsible
for its weaker bond strength. Furthermore, the enhanced metallicity of the
Al-Al bond in AlSc would also contribute to its exceptional ductility.
