  The term "MAX phase" refers to a very interesting and important class of
layered ternary transition-metal carbides and nitrides with a novel combination
of both metal and ceramic-like properties that have made these materials highly
regarded candidates for numerous technological and engineering applications.
Using (Cr2Hf)2Al3C3 as an example, we demonstrate the possibility of
incorporating more types of elements into a MAX phase while maintaining the
crystallinity, instead of creating solid-solution phases. The crystal structure
and elastic properties of MAX-like (Cr2Hf)2Al3C3 are studied using the Vienna
Ab initio Simulation Package. Unlike MAX phases with a hexagonal symmetry
(P63/mmc, #194), (Cr2Hf)2Al3C3 crystallizes in the monoclinic space group of
P21/m (#11) with lattice parameters of a = 5.1739 {\AA}, b = 5.1974 {\AA}, c =
12.8019 {\AA}; {\alpha} = {\beta} = 90{\deg}, {\gamma} = 119.8509{\deg}. Its
structure is found to be energetically much more favorable with an energy (per
formula unit) of -102.11 eV, significantly lower than those of the allotropic
segregation (-100.05 eV) and solid-solution (-100.13 eV) phases. Calculations
using a stress vs. strain approach and the VRH approximation for polycrystals
also show that (Cr2Hf)2Al3C3 has outstanding elastic moduli.
