  Ab initio-calculated ideal strength and toughness describe the upper limits
for mechanical properties attainable in real systems and can, therefore, be
used in selection criteria for materials design. We employ density-functional
ab initio molecular dynamics (AIMD) to investigate the mechanical properties of
defect-free rocksalt-structure (B1) TiN and B1 Ti1-xAlxN (x = 0.25, 0.5, 0.75)
solid solutions subject to [001], [110], and [111] tensile deformation at room
temperature. We determine the alloys' ideal strength and toughness, elastic
responses, and ability to plastically deform up to fracture as a function of
the Al content. Overall, TiN exhibits greater ideal moduli of resilience and
tensile strengths than TiAlN solid solutions. Nevertheless, AIMD modelingshows
that, irrespective of the strain direction, the binary compound systematically
fractures by brittle cleavage at its yield point. The simulations also indicate
that Ti0.5Al0.5N and Ti0.25Al0.75N solid solutions are inherently more
resistant to fracture and possess much greater toughness than TiN, due to the
activation of local structural transformations (primarily of B1 -> wurtzite
type) beyond the elastic-response regime. In sharp contrast, TiAlN alloys with
25% Al exhibit similar brittleness as TiN. The results of this work are
examples of the limitations of elasticity-based criteria for prediction of
strength, brittleness, ductility, and toughness in materials able to undergo
phase transitions with loading. Furthermore, comparing present and previous
findings, we suggest a general principle for design of hard ceramic solid
solutions that are thermodynamically inclined to dissipate extreme mechanical
stresses via transformation toughening mechanisms.
